Question

prove that the lengths of tangents drawn from an external point to a. circle are equal answer​

Answer 1

Answer:

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Step-by-step explanation:

: A circle with centre O; PA and PB 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.

OA⊥PA

OB⊥PB

In △OPA and △OPB

∠OPA=∠OPB (Using (1))

OA=OB (Radii of the same circle)

OP=OP (Common side)

Therefor △OPA≅△OPB (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.

The length of tangents drawn from any external point are equal.

So statement is correct..

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Answer 2

Explaination:


We know that a tangent to the circle perpendicular to the radius through the point of contact.
. ‘ . /_ OPT = OQT=90•
In OPT and OQT,
OT =OT(Common)
OP=OT (Radius of the circle)
/_ OPT = /_ OQT (RHS congruence criterion)
➡️ TP= TQ (CPCT)
Hence,the lengths of the tangents drawn from an external point to a circle are equal

Hope this helps you

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