Q. 214.8( 4 Votes )

If two tangents i A. 3 cm

B.

C.

D. 6 cm

Answer :


Let us consider a circle with center O and AP and BP are two tangents such that angle of inclination i.e. APB = 60°


Joined OA, OB and OP.


To Find : Length of tangents


Now,


PA = PB [Tangents drawn from an external point are equal] [1]


In AOP and BOP


PA = PB [By 1]


OP = OP [Common]


OA = OB [radii of same circle]


AOP ≅△BOP


[By Side - Side - Side Criterion]


OPA = OPB


[Corresponding parts of congruent triangles are congruent]


Now,


APB = 60° [Given]


OPA + OPB = 60°


OPA + OPA = 60°


2 OPA = 60°


OPA = 30°


In AOP


OA PA


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact


AOP is a right - angled triangle.


So, we have





PA = 3√3 cm


From [1]


PA = PB = 4 cm


i.e. length of each tangent is 3√3 cm

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