Question

In the given figure, PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then find ∠APB.
(a) 40° (b) 55° (c) 50° (d) 60°

Answer 1

Answer:

correct option is (c) 50°

Answer 2

Given,

PA and PB are tangents from P to a circle with center O.

∠AOB = 130°

To find,

The measure of ∠APB.

Solution,

We can simply solve this mathematical problem using the following process:

As per the geometry of a circle,

A tangent drawn to a circle at a point on it is always perpendicular to the radius drawn to that point.

This implies,

for the tangents PA and PB to the circle with center O, from point P;

∠OAP = ∠OBP = 90°

Now, according to the question,

Sum of all the angles of the quadrilateral OAPB = 360°

=> ∠AOB + ∠OAP + ∠OBP + ∠APB = 360°

=> 130° + 90° + 90° + ∠APB = 360°

=> ∠APB = 50°

Hence, the measure of ∠APB is equal to 50°.