Practice Set 4.2 Geometric Constructions Class 10th Mathematics Part 2 MHB Solution

Practice Set 4.2

1. Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.…
2. Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.…
3. Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without…
4. Draw a circle of radius 3.3 cm Draw a chord PQ of length 6.6 cm. Draw tangents to the…
5. Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from…
6. Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a…

Practice Set 4.2

Question 1.

Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.

Answer:

Steps of construction:

i. Draw a circle with center P and radius 3.2 cm

ii. Take a point M on the circle, Join PM.

iii. Draw AB ⊥ PM such that AB passes through M, AB is required tangent.

Question 2.

Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.

Answer:

Steps of construction:

i. Draw a circle with center P and radius 2.7 cm

ii. Take a point M on the circle, Join PM.

iii. Draw AB ⊥ PM such that AB passes through M, AB is required tangent.

Question 3.

Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.

Answer:

i. Draw a circle of radius 3.6 cm. Take any point C on it.

ii. Draw chord CB and an inscribed ∠CAB .

iii. With the centre A and any convenient radius draw an arc intersecting the sides of ∠BAC in points M and N.

iv. Using the same radius and centre C, draw an arc intersecting the chord CB at point R.

v. Taking the radius equal to d(MN) and centre R, draw an arc intersecting the arc drawn in the previous step. Let D be the point of intersection of these arcs. Draw line CD. Line CD is the required tangent to the circle.

Question 4.

Draw a circle of radius 3.3 cm Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your observation about the tangents.

Answer:

Here chord = 6.6 = 2 × 3.3 cm = 2 × radius, hence PQ is diameter of the circle.

Steps of construction:

i. Draw a circle with center O, and radius 3.3 cm

ii. Draw a diameter PQ passing through center.

iii. Draw AB ⊥ OQ and CD ⊥ OP , such that AB and CD pass through Q and P respectively.

iv. AB and CD are required tangents.

Observation: AB || CD, i.e. tangents at opposite ends of diameter are parallel.

Question 5.

Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.

Answer:

Steps of construction:

i. Draw a circle with center P and radius 3.4 cm.

ii. Take a point Q outside the circle such that PQ = 5.5 cm

iii. Draw the perpendicular bisector of PQ, which bisects PQ at O.

iv. Taking O as center and OP = OQ as radius, draw another circle, which intersects the previous circle at A and B.

v. Join AQ and BQ, which are required tangents.

Question 6.

Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

Answer:

Steps of construction:

i. Draw a circle with center P and radius 4.1 cm.

ii. Take a point Q outside the circle such that PQ = 7.3 cm

iii. Draw the perpendicular bisector of PQ, which bisects PQ at O.

iv. Taking O as center and OP = OQ as radius, draw another circle, which intersects the previous circle at A and B.

v. Join AQ and BQ, which are required tangents.