Listen NCERT Audio Books to boost your productivity and retention power by 2X.
In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60°. The length of chord AB is
In the given Figure,
As PA and PB are tangents from common external point P, we have
PA = PB
[∵ tangents drawn from an external point are equal]
∠PBA = ∠PAB
[∵ Angles opposite to equal sides are equal]
Now,
In △APB, By Angle sum Property of triangle
∠APB + ∠PBA + ∠PAB = 180°
60° + ∠PAB + ∠PAB = 180°
2 ∠PAB = 120°
∠PAB = 60°
So, We have
∠PBA = ∠PAB = ∠APB = 60°
i.e. APB is an equilateral triangle
so, we have
PA = PB = AB = 5 cm [ As PA = 5 cm ]