Math, asked by Sethuking, 1 year ago

Very urgent please!
Prove that the lengths of tangents drawn from an external point to a circle are equal.

Answers

Answered by Anonymous
1
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Answered by nitthesh7
2
Prove that the lengths of tangents drawn from an external point to a circle are equal.

Given:

PT and QT are two tangent drawn from an external point T to the

circle C 

To prove: PT = TQ

Construction: Join OT.

Proof:

We know that, a tangent to circle is perpendicular to the radius

through the point of contact.

∴ ∠OPT = ∠OQT = 90°

In ΔOPT and ΔOQT,

OT = OT  (Common)

OP = OQ  ( Radius of the circle)

∠OPT = ∠OQT  (90°)

∴ ΔOPT ≈  ΔOQT  (RHS congruence criterion and let ≈ equal to congruent)

⇒ PT = TQ  (CPCT)

Thus, the lengths of the tangents drawn from an external point to a circle are

equal.


Hence Proved



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