OMTEX CLASSES: tangent

10. Draw a tangent to the circle with centre O and radius 3.3 cm from a point A such that d (O, A) = 7.5 cm. Measure the length of tangent segment.

10. Draw a tangent to the circle with centre O and radius 3.3 cm from a point A such that d (O, A) = 7.5 cm. Measure the length of tangent segment.

9. Draw a tangent to the circle from the point L with radius 2.8 cm. Point ‘L’ is at a distance 5 cm from the centre ‘M’.

9. Draw a tangent to the circle from the point L with radius 2.8 cm. Point ‘L’ is at a distance 5 cm from the centre ‘M’.

8. Draw a tangent to the circle from the point B, having radius 3.6 cm and centre ‘C’. Point B is at a distance 7.2 cm from the centre.

8. Draw a tangent to the circle from the point B, having radius 3.6 cm and centre ‘C’. Point B is at a distance 7.2 cm from the centre.

7. Draw a circle having radius 3 cm draw a chord XY = 5 cm. Draw tangents at point X and Y without using centre.

7. Draw a circle having radius 3 cm draw a chord XY = 5 cm. Draw tangents at point X and Y without using centre.

6. Draw a circle of radius 2.7 cm and draw chord PQ of length 4.5 cm. Draw tangents at P and Q without using centre.

Q6. Draw a circle of radius 2.7 cm and draw chord PQ of length 4.5 cm. Draw tangents at P and Q without using the centre.

🎓 Concept: Tangent-Secant Theorem (Alternate Segment Theorem)

To draw tangents without using the centre, we use the property that the angle between a tangent and a chord is equal to the angle in the alternate segment.

If we construct a triangle \( \Delta PQR \) inside the circle, the angle required for the tangent at point P will be equal to \( \angle R \), and similarly for point Q.

Steps of Construction:

Draw a circle with a radius of 2.7 cm.
Take a point P anywhere on the circle.
Using a compass, take a distance of 4.5 cm, place the metal point on P, and cut an arc on the circle to mark point Q. Join chord PQ.
Take any point R on the major arc (the larger side of the circle) and join PR and QR to form \( \Delta PQR \).
Place the compass at point R and draw an arc intersecting sides PR and QR. Keep the same radius.
Place the compass point at P and draw a similar arc intersecting chord PQ. Do the same at point Q intersecting chord QP.
Measure the distance of the arc drawn at angle R. Cut this distance on the arcs drawn at P and Q to replicate \( \angle PRQ \).
Draw a line passing through P and the intersection point of the arcs. This is the required tangent at P.
Draw a line passing through Q and the intersection point of the arcs. This is the required tangent at Q.

Visual Guide:

Fig 1: Rough Figure (Planning the Construction)

Final Construction - Tangents without Centre

Fig 2: Final Construction (Fair Figure)

5. Draw a circle of radius 3.5 cm. Take any point K on it. Draw a tangent to the circle at K without using the centre of the circle.

5. Draw a circle of radius 3.5 cm. Take any point K on it. Draw a tangent to the circle at K without using the centre of the circle.

4. Draw a circle with centre P and radius 3.1 cm. Draw a chord MN of length 3.8 cm. Draw tangent to the circle through points M and N.

4. Draw a circle with centre P and radius 3.1 cm. Draw a chord MN of length 3.8 cm. Draw tangent to the circle through points M and N.

3. Draw a circle of radius 2.6 cm. Draw tangent to the circle from any point on the circle using centre of the circle.

Steps of Construction:

Take a point O as the center and draw a circle with radius 2.6 cm.
Take any point P on the circle.
Draw ray OP.
Construct a line perpendicular to ray OP at point P. This line is the required tangent to the circle.