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##### Source of the problem
I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2018. Subjective Problem no. 2.

5.5 out of 10

##### Suggested Book

‘Challenge and Thrill of Pre-College Mathematics’ by V,Krishnamurthy, C.R.Pranesachar, ect.

Do you really need a hint? Try it first!

$PQ$ and $RS$ are two chords of the circle $C$ , intersecting at the point $O$. See figure: click here.

Given $PO=3$ cm $SO=4$ cm $[\triangle POR]= 7 cm^2$.

From the triangles $POS$ and $QOS$ we have,                 $\angle POR=\angle SOQ$ [Opposite angles]                 $\angle SRP=\angle SQO$ [Angle on the same semi-circle $STP$]                 $\angle QSO= \angle OPR$ [Angle on the same semi-circle $ST’P$]  Therefore the $\triangle POR$ and $\triangle SOQ$ are similar triangles .

$\frac{[\triangle POR]}{OP^2}=\frac{[\triangle SOQ]}{SO^2}.$ $\Rightarrow [\triangle SOQ]=\frac{SO^2}{PO^2}\cdot [\triangle POR]$=$\frac{4^2}{3^2}\cdot 7=12\frac{4}{9}$.(Ans.)

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