Question

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

Answer 1

To prove PT=QTPT=QTProof: Consider the triangle OPTOPT and OQTOQT.OP=OQOP=OQ∠OPT=∠OQT=90∘∠OPT=∠OQT=90∘OT=OTOT=OT (common side)Hence by RHS the triangles are equal.Hence PT=QTPT=QTHence Proved.

Answer 2

To prove PT=QT

Proof: Consider the triangle OPT and OQT.

OP=OQ

∠OPT=∠OQT=90∘

OT=OT (common side)

Hence by RHS the triangles are equal.

Hence PT=QT

Hence Proved.