Question

State the following statement is True or False

The length of two tangents drawn from an external point to a circle are unequal.

• A. True
• B. False

Answer 1

The correct option is B False

The lengths of tangents drawn from an external point to a circle are equal.

Proof:

We are given a circle with centre O, a point P lying outside the circle and two tangents PQ, PR on the circle from P (see Fig.)

We are required to prove that $PQ=PR$.

For this, we join $OP,OQ$ and $OR$.

Then $\angle OQP$ and $\angle ORP$ are right angles, because these are angles between the radii and tangents.

Now in right triangles $OQP$ and $ORP$,

$OQ=OR$ (Radii of the same circle)

$OP=OP$ (Common)

Therefore, $\Delta OQP\cong \Delta ORP$ (RHS)

This gives $PQ=PR$ (CPCT)

This implies that the given statement is false because it states that "The lengths of tangents drawn from an external point to a circle are unequal."