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Length of Tangents Drawn from an External Point

Prove that th...

Question

Prove that the length of tangents drawn from an external point to a circle are equal.

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Solution

We know that the radius and tangent are perperpendular at their point of contact
∴ ∠OAC = ∠OBC = 90^∘
Now, In △OCA and △OCB
∠OAC = ∠OBC = 90^∘
OA = OB (Radii of the circle)
OC = OC (Common)
By RHS congruency
△OCA ≅ △OCB
∴ CA = CB

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