Q. 105.0( 2 Votes )

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

Answer :

Let us consider a circle with center O.

TP and TQ are two tangents from point T to the circle.

To Proof : PT = QT

Proof :

OP ⏊ PT and OQ ⏊ QT

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

∠OPT = ∠OQT = 90°

In △TOP and △QOT

∠OPT = ∠OQT

[Both 90°]

OP = OQ

[Common]

OT = OT

[Radii of same circle]

△TOP ≅ △QOT

[By Right Angle - Hypotenuse - Side criterion]

PT = QT

[Corresponding parts of congruent triangles are congruent]

Hence Proved.

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PREVIOUSFill in the blanks.(i) A line intersecting a circle in two distinct points is called a ……..(ii) A circle can have ………..parallel tangents at the most.(iii) The common point of a tangent to a circle and the circle is called the ………..(iv) A circle can have ………..tangents.NEXTProve that the tangents drawn at the ends of the diameter of a circle are parallel.

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