If PA and PB are tangents from an outside point P. Such that PA = 10cm and ∠APB = 60°. Find the length of cord AB.

 Given : PA and PB are tangents of a circle, PA = 10 cm and ∠APB = 60°

Let O be the center of the given circle and C be the point of intersection of OP and AB

In ΔPAC and ΔPBC

PA = PB  ( Tangents from an external point are equal)

∠APC = ∠BPC ( Tangents from an external point are equally inclined to the segment joining center to that point)

PC = PC ( Common)

Thus ΔPAC  ΔPBC (By SAS congruency rule) ..........(1)

∴ AC = BC

Also ∠APB = ∠APC + ∠BPC

∠ACP + ∠BCP = 180°

Now in right triangle ACP

∴ AB = AC + BC = AC + AC  ( AC = BC)

⇒ AB = (5 + 5) cm = 10 cm

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