Question

In the figure, PQ and PT are tangents. AB is a third tangent touching the circle at C. If PQ $=$ 35cm, then the perimeter of $△PAB$ is

• A. $70cm$
• B. $35\sqrt{2}cm$
• C. $35\sqrt{3}cm$
• D. $35cm$

Answer 1

The correct option is A $70cm$

$\Rightarrow$ $PQ=35cm$ [ Given ]

$\Rightarrow$ $PQ=PT$ [ Tangent from $P$ ] ---- ( 1 )

$\Rightarrow$ $CA=AQ$ [ Tangents from $A$ ] ---- ( 2 )

$\Rightarrow$ $BC=BT$ [ Tangents from $B$ ] ---- ( 3 )

$\Rightarrow$ Perimeter of $△PAB=PA+PB+BC+CA$

$=PA+AQ+PB+BT$ [ From ( 2 ) and ( 3 ) ]

$=PQ+PR$

$=PQ+PQ$ [ From ( 1 ) ]

$\Rightarrow$ Perimeter of $△PAB=2PQ$

$=2\times 35cm$

$=70cm.$