Question

The diagram below shows tangent lines and circles. Find $PD$.

Short answer

The value of $PD=8·2$

Step-by-step solution

Step 1. Given information.

The figure here given is,

Step 2. Consider circle I.

In the given figure, $AP$ and $BP$ are given as the tangents to the circle.

Use the fact that if $BP, AP$ are tangents to a circle from an external point to a circle then $BP= AP$,

$BP=AP=8.2$

Step 3. Consider circle II.

$CP$ and $BP$ are tangents to the circle.

As it is known that tangents drawn from any point external to the circle onto the same circle are equal,

$CP=BP=8.2$

Step 4. Consider circle III.

$PD$ and $PC$ are tangents to the circle.

As tangents drawn from an external point to a circle are equal,

Therefore, $PD=PC=8.2$