2 equal tangents PA and PB are drawn from an external point

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2 equal tangents PA and PB are drawn from an external point P on a circle with centre O. What is the length of each tangent, if P is 12 cm from the centre and the angle between the tangents is 120°?

As per the given in question , we draw a figure of a circle with centre O

∠APB = 120°
OA = OB = radii
∴ ∠APO = ∠OPB = 60°
∴ From ∆ OAP,

cos 60° =	AP
	OP

⇒	1	=	AP	⇒ AP = 6cm.
	2		12