Q. 455.0( 3 Votes )

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


A. 5√2 cm

B. 5 cm

C. 5√3 cm

D. 7.5 cm

Answer :

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 ]

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