INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

March 13, 2019

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.

area of triangle- figure

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 \(\triangle QOS = \frac{112}{9}\).

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
enter