Question

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

Answer 1

Answer:

Statement: The tangents drawn from an external point to a circle are equal.

Given:

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

To Prove: PT=TQ

Construction:

Join OT.

Solution:

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

∴∠OPT=∠OQT=90

∘

In △OPT and △OQT,

∠OPT=∠OQT(90

∘

)

OT=OT (common)

OP=OQ (Radius of the circle)

∴△OPT≅△OQT (By RHS criterian)

So, PT=QT (By CPCT)

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

Answer 2

Answer:

hope this will help you ❤️