Q. 93.7( 12 Votes )

If two tangents i A.

B. 6 cm

C. 3 cm

D.

Answer :


Given : A circle with center O and PA and PB are two tangents to the circle at point A and C from an external point P such that APC = 60° [i.e. angle of inclination between two tangents] .


To Find : AP and PC


In OAP and OCP


AO = OC [ radii of same circle]


OP = OP [ common ]


AP = PC [ tangents through an external point to a circle are equal]


OAP OPC [ By Side Side Criterion]


APO = OPC [Corresponding parts of congruent triangles are equal] [1]


Now, APC = 60° [Given]


APO + OPC = 60°


APO + APO = 60° [By 1]


2AP0 = 60°


APO = 30°


Now, OA AP [ As tangent at any point on the circle is perpendicular to the radius through point of contact]


OAP = 90°


So AOP is a right-angled triangle


And we know that,



So,


[As OA is radius and equal to 3 cm]



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