Construct a pair of tangents to circle whose radius is 6.5 cm are inclined to each other at angle of 30 degree.

Dear Student

The tangents can be constructed in the following manner:

Step 1

Draw a circle of radius 6.5 cm and with centre as O.

Step 2

Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A.

Step 3

Draw a radius OB, making an angle of 150° (180° − 30°) with OA.

Step 4

Draw a perpendicular to OB at point B. Let both the perpendiculars intersect at point P. PA and PB are the required tangents at an angle of 30°.

Justification

The construction can be justified by proving that ∠APB = 30°

By our construction

∠OAP = 90°

∠OBP = 90°

And ∠AOB = 150°

We know that the sum of all interior angles of a quadrilateral = 360°

∠OAP + ∠AOB + ∠OBP + ∠APB = 360°

90° + 150° + 90° + ∠APB = 360°

∠APB = 30°

This justifies the construction.

Regards