Question

Prove that the tangents drawn to a circle from a point in the exterior of the circle are congruent.

Answer 1

To prove: Tangents drawn to a circle from a point in the exterior of the circle are congruent.

The exterior point as shown in the figure is T.

The centre of the circle is O.

To show:$PT=QT$

Consider $\Delta PTO$ and $\Delta QTO$

$OP=OQ$(radii of the circle)

$OT=OT$(common side)

$\angle OPQ=\angle OQT=90$(Tangent to the circle is perpendicular to the radius at the point of tangency.)

Hence by RHS triangles are equal that is $\Delta PTO\cong \Delta QTO$

Therefore $PT=QT$

Hence, Tangents drawn to a circle from a point in the exterior of the circle are congruent.