Find S P if T P=18 {\cm}, R Q=4 {\cm} and T R=6 {\cm}.

ICSE Class X Math 2016 Solved Paper - Question 25

In the given figure $P Q R S$ is a cyclic quadrilateral $P Q$ and $S R$ produced meet at $T$ .

Question : 25 of 57

Marks: +1, -0

Find

S P

T P=18 {\cm}, R Q=4 {\cm}

and

T R=6 {\cm}

Solution:

In similar triangles

∆ {\TPS}

and TRQ

\;\;{T P}/{T R}=\;{P S}/{R Q}

\;\;{18}/{6}=\;{P S}/{4}

\; {\PS}= \;{72}/{6}

\;\; = 12 {\cm} .

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