# 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 isA. 5√2 cmB. 5 cmC. 5√3 cmD. 7.5 cm

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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