From a point P, two tangents PA and PB are drawn to a circle with centre O If OP - Maths - Circles

Question

From a point P, two tangents PA and PB are drawn to a circle
with centre O If OP = diameter of the circle, show that the
triangle APB is equilateral

Lalit Mehra · Accepted Answer

AP is the tangent to the circle âˆ´ OA âŠ¥ AP (Radius is perpendicular to the tangent at the point of contact) â‡’ âˆ OAP = 90Âº In Î” OAP, $\sin ∠ O P A = \frac{O A}{O P} = \frac{r}{2 r} [O P = D i a m e t e r o f t h e c i r c l e] ∴ \sin ∠ O P A = \frac{1}{2} = \sin 30 °$

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that the triangle APB is equilateral.