Circle : Chord And Arc
Class 8th Mathematics (new) MHB Solution
Class 8th Mathematics (new) MHB Solution
Practice Set 17.1- In a circle with centre P, chord AB is drawn of length 13 cm, seg PQ ⊥ chord AB, then…
- Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre…
- O is the centre of the circle. Find the length of the radius, if the chord of length 24…
- C is the centre of the circle whose radius is 10 cm. Find the distance of the chord…
Practice Set 17.2
- In a circle with centre P, chord AB is drawn of length 13 cm, seg PQ ⊥ chord AB, then…
- Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre…
- O is the centre of the circle. Find the length of the radius, if the chord of length 24…
- C is the centre of the circle whose radius is 10 cm. Find the distance of the chord…
Practice Set 17.1
Question 1.In a circle with centre P, chord AB is drawn of length 13 cm, seg PQ ⊥ chord AB, then find l(QB).
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAABoCAYAAADcm/8NAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA5/SURBVHja7V0PKGTdG562b9Nq26+NtBJtJNJKJNJKJBJNJBKJRBrJJNJIpJVItK202kgkmkybSTaRTKKJJhJNK5Fsm02k2TabbPL8znvs/r5da9eMuTNz77hP3WT86Z7znPOe95z3fZ+jgIw7B4XcBTLpMmTSZcikuwHOz89xdHSEjY0NrK+tYWN9nX99bzbDYrHgQiZdmjhkpBoXF9HX14fCggIEBgTgqb8/cnNzUVZWhvz8fDQ2NKC5qYk/L5qbUa1Wo6iwkP88KzOT/010ZCQ0dXUYGhzC0tISPn/+LJMuBpyenmKdzVatVoucrCzcv3cPiYmJqK2pQXd3Nyd+ZHgYU+/ewcxm9/bWFnZ3dvD15IT/7devX/nXz2yW77DPt9jP19jMn5yYwOjICEbY09rSigpVBfx9/fDEy5sPmPHxcexsb+Pbt28y6c7Ahw8foNPp0NTYiLjYWAQ+fYqG+gZMTk7C/N6ME0aoI3D8fVkY045xqxDg54fUlBS0trbyQXV8fCyTLjRo5lWoVMhUKhEeFoZ6TT2f5a7EktEIVXk5QoKCkKXMRDlbHhbm52XS7QGZXVpzaUY9j4tDeWkZN8FihGFuDsr0dCTEx/NncHBQJt0WkInu6OhAMJtBJSUl3Jk6+3Ym9jHK8fHjR/QwfyInJwcJz5+zdxcX+aIjnch+3dPDHbKiwiKYTCZJEH0daHv4jvkZSQkJCH/2jDuUFxeu3xSKivT+/n7eOdnMC6ctkjthZnoGkWwLmMAGwPTMjEw6OWO0ZgcFBorOFAqN9rY27vSR9+8qb9/lpDfW1+PhA080su3XV7Zfvgv49OnT5aER22qOvx2/O6STs6PMUPKTMsOc4U6QfRXDbI0PDgrm2zxnHvK4hHTa2gQFBqGUeeVnZ9LwyB05+NNS0xAaGord3V33JL3lxQs8CwvD6MjonSb7KigG4P34MfTjjjf3TiWdZvYDDw8YDHfTnN8E2qoqFAp0tLW7B+l0UuXj5Q2z+b3M7l+g1+s58XW1tdImPTc7m5t0CpTIuBkLCwvw9vJCG9veSZL0vNxcvgeXSgRKLKAwr5+vLw/jSop0SkCIjorCPvNQZdiOxcXFywOroSFpkF5bXc3X8L29PZk9O0BOL8XtaQCImvRhNjIpYDLH9uMyBOjP4WHcY84dZeqIknRKNKRw6ODAgMyWgKisqEBkRIQgUTpBSafTNUoeKCstlVlyACj6WJhfIC7SKVcsJDhYZsdB2N3Z5csmxehFQfry0hI8PTywYTbL7DgQ2tFRHp2jLF6Xkk4RItqLV7F1R4bjkZuTg1I7llBBSKfccDpIkOEcUBo2nX/Mzs66hnSq+qB1fNLOdUaGbajXaLjT7BLSh4aGecanDOdif3+fL6njtwjF2kX62ekpHno8wJLRvZIYpQKKxCUnJTmXdFrLU5KS5d53ESgoQybe1tluF+lhoaGY0Ovl3nchMjMy+OMU0hcWFhEVEcHLjmS4Dqurq8hSKnmNvcNJV6Zn8LIjGa5HTHQ0WlpaHEs6Hcb4+fjAaDRKtJvOsDk1hLq0EDx9loGWsVnoX2lQWaZC/4r0hAeowLOqqsqxpFPGZl5OLr5IWJnh/GAZdfH3oPCrx8bxCSz7OzD15rLdSCjy+sVZFfsnUBpaSnKy1XV/tyI9NTkFrTaYE3HiGP2VUVBk/XyotIFShQKeUR2QWq4PpU9TpazDSH/i7cMrMKWNA/SWh0ORrvvps3XkK/6BT8IbWCTWGo1Gw8z8C8eQToIAucy0b25uugfpyonLbz+voLciGyHBpehb+SK51szPz6O8rBxHh4fCk05VpWq1movzSBuHGCgLgsK3FKPj7zBrmMOMwYTtQ2m2hmIgUZGRWGNbOMFJJ30VEviRPg7wpvwZFPG9ODg9cwv9OEqweKvTCU+6z2Mv1Kir3aCLTjBUGwtF3qwbtOUS5MGTsIPgpMdERaO/r0/i3XOOjwt9SL2vgEKRibfmT5CeGtzvaGtt5fVwgpJOGipUSz2/IG7JLGtwsG7ASFszOtoHMb9z5BbmnUw7HdRcMJ4EI50KF8hDtOWcV4bzQCqXlRWVNzrZNpG+YjLxUqVP+/tyD4sQNCkpTfrw4EBY0ilNxx1Ipxz9zo5OFBcXY2R4xC1IJy0bmfS/4E1vL68D//GsWrG/FTsohUom/S+gerufSaf1UCbdzUmnmrDY6GhOuFg1XG2FQ8w7VbFwR479c3cAlQcR6e4CCrEKTjoJ5JNYECXbuwNIo92dSKegi7qy8saSJ5tafPbtG4qLitym7tzdZjolqZIM6U3lzLYfw7J10F1qz92NdNLo67Qib9HmFpOsZ7NbRNncj/SC/HyrJqTNLSbz3tzcLJMuQlBbrAmG2dziATaSXjAzIgaxepn0/0DBsCfe3licXxCedBKtJQ9+WyDRG5l0YUBnKKRLQxcNCk464aGHB1dEkEkXD8jPqq+vt+p3b5kCnYzuV69k0kUEuiSQlKQdRvrY2Bgz8aX8FkOZdNeDJFgTExKsvg/uVi2mID0l4RkXpVrW5F6kv+zq4n7W+Q0ZM3aRTkhJTmF7wkGZdBGArh5tsHI9t4t0ukKLsi+/fJFeYYA7kU6payRDsmJacTzpBNIrnXXxHWN3nfSqykour24L7GrxQP8AP6GTSXcNLBYL0lJT+cXDTiOdrsikaklX32x8V0mvr9PwUiZbYXeLSQGB5C9k0p0LSmSJi4nlnrvTSafCuUeenpJMLJQy6bU1tQgODLrV3wrSYjqdS05MlEl3EtaYxx4SFIx5w+0qjQRpMR0K0F5RasJDUiW9rKQU0ZFRt/57wVo8NzvLEyykdA2XFEmnvD5/Pz/mud9e70fQFleoVLcWqZVJvxlfvosv975+bdf/sbvFZz/lUtDBfxJb2ylXSyZdeBQWFCI7J8/u/2OfIPCyBr5BtVj+6SSWbg98GhCACQlUjMxMT0uG9FcvX+I+3di0/A7zE0PoHdHDuLGH/R0TJvp1mDJZnEH6CbSZfrzTovu2fntBukSOBGvFjDGtlr//wQ3FAa7G4sIifJ88wcqyEd92Z1EVSqVY/micNmFjaRztZYWI9otFjW7VKnGF25O+2YX4gia0lUThnwdVuCpbp2Lre/zzeF4YQWaf7gkXw0P1XvSQJNqPOrZQtk6urqxw8sXynvRQv5Hl9Pr3MVfc/oH1VhXCFJX4+bacnfZwKO4l482mA0mfU2ehamITJ8dzKFDcQ/Lw7/VtmUol71SKxtEgKCoqcvlDpckUL/Dx9v6lgDEsNISrbIjhHemhfLeI8HD+blQ/+B8uYGwoRJBChZ8Pv09G0tnvBqPW8NlBpH/sRWJxN37Irc3WhkLxbzWuuySblKIj2ctbvqtF057etc+l57m3twtPjwe8U5/HRLGlaFsE73b+/0QIM7OQdNc87Yh+xQWWGgvgp1BC9+mY9es+jAPViGfmXqmZxBEcNNPXmrKRqe7A1Nom3r/fwtJQFfxZ5yUO/b42UpYNzXS6YUg0OP8Ak3GVOZtv0dXRjvVdcckM0TITFxMDdZX62p+bmvPwWBGBF+/mYTSOoyM/DamJhXizbp0Inu2kf51AbmENOocMWF1b5Wfua8vjUEcxM/mwGn9KjKZqSrrr5cTFSRenpgFo2rsxOG7A+voKTEtT6G7qQo9WHLGDjY11Xjr250yY68372UIdAj1i0DBxs1NqI+kXWKlXobRzElfH1PFEJTxp/R76s5Qureu0Trnqau2L96+RHl+AzoVf172LvbcoSi9A3ZhrZYANhjl+n2pXR+dff8/UXIIQRvraL58uIoX1v3++DjdpedpE+sXGG8TfD0S8Sndl7TjHe20Nwskp8iqB/i8nsSR5RXe4OV/5YQctoY8QVqHH2TU/XWvPwrNnuZiwuIZwqjYN8A+w4q70fWgLYpgvkoSx41PmA5zh8/4W9Jo49lkkNFOCz3Rh0P2qG/+wAdLR6cQAzVYb65THyBn4w9nBUh18fP2QqXOuhj3Vkhfk5fHz9KmpqRt//3hlFLXpgbj3JBaVPXrMz0+iR5WK+JQCvFmxLiXdZcdRFB4MDgpGRno6V5Z2OKaLGemeyBn+gxlaa8LjR15I6HVewIiUPcLDwrhJd2aCqUvPIMmzJ4FhX2burRWovzV2OvGQWZfkzutVNE7GctmguI+MMYtT2k7VKHRc3djg/LJvURw8z8zM8BGflJBglXT17bCP9gDmczytueIAEQ7R89wPikfFMDi4GNcwNwevR//yhMY1FylviibacCnm18HPmOlA4qMj4vJrnQhWeCAsrwcbx9/Z/XKI+a4ixEakotPouP26aXmZn1VQImOfiwWVRRdiooS/kqIixMfFoVqtxt6esOSfmUegiohESkoiIpKUKG58hVeNLzHroJjLktHIBzFtVak9NLhdDdHGFSmtOic7GwnP45GZoYTZbBb0/1umq3ioUuGjwca58O9Pnji9f2xMzOU1G0dHEAtEH0xeXFy8nPmMfJr9o6OjVhfq3YSLbQN6KkqQo25CS8sApqeN2Dq8vYk/ZMR2dXYhgG39SP+FNPfEGF6WTNrI3u4etFot8tme1sfLi38lB/Dw0P5LV47299i2cR8Wy4lNYv8kwbKzvQ29Xo+0lBQeuSNTPqYdu1HLTSbdRmzvbKO/r59n4AYHBvIwJN1oQJcE0swSyhJcBa3HFP3S6XTo6upCUWERHty/j/S0ND4ghRiAMunWzFJmUkk0jzxjEtqhYr4mtgfW1GlQqargd5rQ9aCkkXNoRYYMzV5yJrc2N7klocGkYmsy3XtWV1vHCQ4JCuKfGQwGUThmd470qyDCSJGhubEJ6WwvTIc/dA9pbU0NaqqruVWgSk/6evWhzykoRJfR/3hKiouRm5XND4/Iv7C4wS3Sbkf6daCTP5rlZPppC0UpSIvXPPQ5HY1S7r6YvG2ZdBky6TJk0mXIpMu4Dv8DbrEDE6OlJkwAAAAASUVORK5CYII=)
Answer:We know that,
The perpendicular from the centre of a circle to a chord bisects the chord.
Therefore, it is given that,
AB=13 cm
PQ perpendicular to AB
|(QB) = AB/2
| (QB) = 13/2
| (QB) = 6.5 cm
Question 2.Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre if the length of the chord is 48 cm.
![](data:image/png;base64,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)
Answer:As we know that, the perpendicular from the centre of a circle to a chord bisects the chord.
Therefore, OP perpendicular to CD and OP bisects the CD. Therefore, it makes a right angle triangle, which is ∆OPD. We have OD=25 cm and PD=48/2=24 cm.
By Pythagoras theorem,
OD2 = OP2 + PD2
OP2 = OD2 - PD2
OP2= (25)2 - (24)2
OP2 = 625 – 576
OP2 = 49
OP = 7 cm
Therefore, distance of the chord from the centre is 7 cm.
Question 3.O is the centre of the circle. Find the length of the radius, if the chord of length 24 cm is at a distance of 9 cm from the centre of the circle.
![](data:image/png;base64,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)
Answer:![](data:image/jpeg;base64,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)
As we know that, the perpendicular from the centre of a circle to a chord bisects the chord.
So let P is the point, which bisects chord AB. So OP is perpendicular, it makes a right angle triangle ∆OPA.
Now we have OP = 9cm and AP as 12 cm
So by Pythagoras theorem,
AO2 = AP2 + PO2
AO2 = (12)2 + (9)2
AO2 = 144+81
AO2 = 225
AO = 15 cm
Length of radius is 15 cm.
Question 4.C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.
Answer:![](data:image/jpeg;base64,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As we know that, the perpendicular from the centre of a circle to a chord bisects the chord.
So here we have C as a centre where CP is perpendicular on AB which bisects the chord AB and radius as CA = 10 cm and chord length = 12 cm, so AP=6cm.
It makes a right angle triangle ∆CPA.
Therefore, by using Pythagoras theorem, we have,
AC2 = CP2 + AP2
We have to find CP so
CP2 = AC2 - AP2
CP2 = (10)2 – (6)2
CP2 = 100 – 36
CP2= 64
CP = 8 cm
Therefore, a distance of the chord from the centre is 8 cm.
In a circle with centre P, chord AB is drawn of length 13 cm, seg PQ ⊥ chord AB, then find l(QB).
Answer:
We know that,
The perpendicular from the centre of a circle to a chord bisects the chord.
Therefore, it is given that,
AB=13 cm
PQ perpendicular to AB
|(QB) = AB/2
| (QB) = 13/2
| (QB) = 6.5 cm
Question 2.
Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre if the length of the chord is 48 cm.
Answer:
As we know that, the perpendicular from the centre of a circle to a chord bisects the chord.
Therefore, OP perpendicular to CD and OP bisects the CD. Therefore, it makes a right angle triangle, which is ∆OPD. We have OD=25 cm and PD=48/2=24 cm.
By Pythagoras theorem,
OD2 = OP2 + PD2
OP2 = OD2 - PD2
OP2= (25)2 - (24)2
OP2 = 625 – 576
OP2 = 49
OP = 7 cm
Therefore, distance of the chord from the centre is 7 cm.
Question 3.
O is the centre of the circle. Find the length of the radius, if the chord of length 24 cm is at a distance of 9 cm from the centre of the circle.
Answer:
As we know that, the perpendicular from the centre of a circle to a chord bisects the chord.
So let P is the point, which bisects chord AB. So OP is perpendicular, it makes a right angle triangle ∆OPA.
Now we have OP = 9cm and AP as 12 cm
So by Pythagoras theorem,
AO2 = AP2 + PO2
AO2 = (12)2 + (9)2
AO2 = 144+81
AO2 = 225
AO = 15 cm
Length of radius is 15 cm.
Question 4.
C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.
Answer:
As we know that, the perpendicular from the centre of a circle to a chord bisects the chord.
So here we have C as a centre where CP is perpendicular on AB which bisects the chord AB and radius as CA = 10 cm and chord length = 12 cm, so AP=6cm.
It makes a right angle triangle ∆CPA.
Therefore, by using Pythagoras theorem, we have,
AC2 = CP2 + AP2
We have to find CP so
CP2 = AC2 - AP2
CP2 = (10)2 – (6)2
CP2 = 100 – 36
CP2= 64
CP = 8 cm
Therefore, a distance of the chord from the centre is 8 cm.
Practice Set 17.2
Question 1.The diameters PQ and RS of the circle with centre C are perpendicular to each other at C. State, why arc PS and arc SQ are congruent. Write the other arcs, which are congruent to arc PS
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)
Answer:As we know that, according to the theorem of the circle, two arcs are congruent, if their central angles are congruent, so arc PS and arc SQ are congruent because the angles between the chords are same and both are at 90° of the centre.
The other arcs, which are congruent to arcs PS, are
arc PS ≅ arc PR ≅ arc RQ because if two arcs of a circle are congruent, then their corresponding arcs are also congruent.
Question 2.In the adjoining figure O is the centre of the circle whose diameter is MN. Measures of some central angles are given in the figure. Hence, find the following
![](data:image/png;base64,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)
(1) m∠AOB and m∠COD
(2) Show that arc AB ≅ arc CD
(3) Show that chord AB ≅ chord CD
Answer:(1) In given figure, we can see that
∠NOC + ∠COD +∠DOM = 180° (linear pair)
35° +∠COD+100° =180°
∠COD = 180° - 135°= 45°
So ∠COD and ∠AOB = 45°
(2) arc AB ≅ arc CD because the arcs are of equal measure 45° each angle and equal angle made equal sector.
(3) chord AB ≅ chord CD because corresponding chords of congruent arcs are congruent.
The diameters PQ and RS of the circle with centre C are perpendicular to each other at C. State, why arc PS and arc SQ are congruent. Write the other arcs, which are congruent to arc PS
Answer:
As we know that, according to the theorem of the circle, two arcs are congruent, if their central angles are congruent, so arc PS and arc SQ are congruent because the angles between the chords are same and both are at 90° of the centre.
The other arcs, which are congruent to arcs PS, are
arc PS ≅ arc PR ≅ arc RQ because if two arcs of a circle are congruent, then their corresponding arcs are also congruent.
Question 2.
In the adjoining figure O is the centre of the circle whose diameter is MN. Measures of some central angles are given in the figure. Hence, find the following
(1) m∠AOB and m∠COD
(2) Show that arc AB ≅ arc CD
(3) Show that chord AB ≅ chord CD
Answer:
(1) In given figure, we can see that
∠NOC + ∠COD +∠DOM = 180° (linear pair)
35° +∠COD+100° =180°
∠COD = 180° - 135°= 45°
So ∠COD and ∠AOB = 45°
(2) arc AB ≅ arc CD because the arcs are of equal measure 45° each angle and equal angle made equal sector.
(3) chord AB ≅ chord CD because corresponding chords of congruent arcs are congruent.