Question

In the given figure, from an external point $P$, tangent $PX$ and $PY$ are drawn to a circle with centre $O$. $AB$ is another tangent to the circle at $C$ and $PX=14cm$, then find the perimeter of $△PAB$.

Answer 1

REF.Image

Given $\to$ PX= 14 cm

To find $\to$ Perimeter of $△PAB$

$PX=PY=14cm$

(Length of tangents from the

same external point to the same

are equal)

Let $AX=xcm$

$AX=AC=xcm$ (Length of tangents from an external point to the

same circle are equal)

Similarly, Let $BY=ycm$

$BC=BY=ycm$

Now, $AP+AX=PX$

$AP=PX-AX$

$AP=(14-x)cm$

Similarly, $PB=(14-y)cm$

Perimeter of $△PAB=AP+PB+AB$

$=(14-x)cm+(14-y)cm+(x+y)cm$

$=28cm$

Perimeter of $△PAB=28cm$