In Fig. 10.81, AP is a tangent to the circle with centre O such that OP = 4 cm and ∠OPA = 30°. Then, AP =

Question

In Fig. 10.81, AP is a tangent to the circle with centre O such that OP = 4 cm and ∠ OPA = 30 ° . Then, AP =

Philoid · Accepted Answer

Given:

OP = 4 cm

∠OPA = 30°

Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆POA is right-angled at ∠OAP (i.e., ∠OAP = 90°).

Now we know that,

Therefore,

⇒ AP = 2√3 cm

Hence, AP = 2√3 cm