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# Area of Triangle - ISI BStat 2018 Subjective Problem

Here is a problem based on the area of triangle from ISI B.Stat Subjective Entrance Exam, 2018.

## Sequential Hints:

Step 1:

Draw the DIAGRAM with necessary Information, please! This will convert the whole problem into a picture form which is much easier to deal with.

Step 2:

Power of a Point - Just the similarity of $\triangle QOS$ and $\triangle POR$

By the power of a point, PO . OQ = SO . OR . We know SO = 4; PO = 3.

Let, OQ be $x$. Hence we get the following:

SO = 4; PO = 3; OQ = $x$; OR = $\frac{3x}{4}$.

Step 3:

Assume $\angle QOS = \theta$ .

Now, compute the area in terms of $x$.

Area of $\triangle QOS = 2x\sin{\theta}$.

Area of $\triangle POR = \frac{9x\sin{\theta}}{8}$.

Therefore, we get the following that $\frac{\triangle QOS }{\triangle POR } = \frac{16}{9}$.

Hence the Area of $\triangle QOS = \frac{112}{9}$.

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