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Question

State the following statement is True or False
The length of two tangents drawn from an external point to a circle are not equal.

A
True
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B
False
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Solution

The correct option is B False


We are given that the length of tangents drawn from any external point are not equal. But we will prove that the length of tangents drawn from any external point are equal.

Proof is as follows:

Given: A circle with centre O; PA andPB are two tangents to the circle drawn from an external point P.

To prove: PA=PB

Construction: Join OA,OB, and OP.

It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.

OAPA (1)

OBPB (2)

In OPA and OPB

OPA=OPB (Using (1) and (2) they are equal to 90o)

OA=OB (Radii of the same circle)

OP=OP (Common side)

Therefor OPAOPB(RHS congruency criterion)

PA=PB

(Corresponding parts of congruent triangles are equal)

Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.

So the asked statement is incorrect.



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