Question

If AB, AC, PQ are tangents in the figure given below and AB = 5 cm, find the perimeter of $\Delta APQ.$

Answer 1

Let PQ touch the circle at the point R.

We know that tangents drawn from an external point to a circle are equal in length.

AB = AC = 5cm

Similarly, $BP=PX,XQ=QC$
Now, perimeter of $\Delta APQ=AP+PQ+AQ$

$=AP+XP+QX+AQ$

$=(AP+PX)+(AQ+XQ)$

$=(AP+BP)+(AQ+XQ)$

$=(AP+BP)+(AQ+QC)$

$=AB+AC$

$=5+5=10$

Perimeter of $\Delta APQ=10cm$