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