Question

prove that the tangents drawn from an external point to a circle 1 are equal
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Answer 1

Answer:

your solution attached in the above pic

Answer 2

Step-by-step explanation:

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 equal.