Question

Prove that “ the tangent drawn from an external point to a circle are eqaul”.​

Answer 1

Answer:

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Answer 2

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Two tangents AP and AQ are drawn from a point A to a circle with centre O.

${\bold{\pink{\underline{\pink{To}\:\purple{Pr}\blue{ove}\red{:-}}}}}$

• AP = AQ

$\sf\green{{CONSTRUCTION:-}}$

join OP ,OQ and OA .

${\bold{\pink{\underline{\red{P}\purple{ro}\green{of}\orange{:-}}}}}$

AP is a tangent at P and OP is the radius through P.

∴ OP ⟂ AP

Similarly, OQ ⟂ AQ

In the right ∆ OPA and OQA

OP = OQ ( radii of the same circle )

OA = OA ( common )

∠ OPA = ∠OQA ( since AP and AQ are tangent to the circle )

∴ ∆OPA ≅ ∆ OQA ( by RHS congruence )

Hence, AP = AQ