Question

prove that the tangents drawn to an circle from an external point are equal​

Answer 1

Correct Question:-

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

Solution:-

Given :- Let circle Be with the centre O & P be a point outside the circle PQ & PR are two Tangents to circle intersecting at point Q & R respectively.

To prove:-

lengths of Tangents are equal

=> PQ = PR

Construction:-

Join OQ, OR & OP

OQ | PQ --( Tangent at any point of a circle is perpendicular to the radius through the point of contact)

So, ∠OQP = 90°

Hence , ∆ OPQ is right Triangle

Same as PR is a Tangent

& OR | PR

=> ∠ORP = 90°

Now, in ∆ OPQ & ∆ORP

• ∠OQP = ∠ORP ---(Both 90°)
• OP = OP ----(Common)
• OQ = OR ----(Radius)

• ∆OQP ~ ∆ORP ----( RHS Congruency)
• PQ = PR ( CPCT) Hence Proved!

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