Question

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

Answer 1

PT and QT are two tangents drawn from an external point T to the circle ( O , R )

To prove :- PT = QT

Construction :-

Join QT

Solutions:-

We know that a tangent to a circle is perpendicular to the radius through the point of contact.

:- Angle OPT = Angle OQT = 90⁰

In angles OPT and angles OQT,

Angles OPT = Angles OQT ( 90⁰ )

OT = OT ( Common )

OP = OQ ( Radius of a circle )

:- Angles OPT = Angles OQT ( By RHS criterian )

So, PT = QT ( By CPCT )

Hence, the tangent drawn from an external point to a circle are equal.

I hope this will help you dear..

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