In the circle given below, let OA=1 unit, OB=13 units and PQ OB.

Question

In the circle given below, let $OA=1$ unit, $OB=13$ units and $PQ\perp OB$. Then, the area of the triangle $PQB$ (in square units) is

Accepted Answer

$OB$ is a diameter, so radius $=6.5$; let $C$ be the centre. $PC=OC=6.5$, and $AC=OC-OA=5.5$.

$$PA^2=PC^2-AC^2=(6.5-5.5)(6.5+5.5)=1\times12=12\ \Longrightarrow\ PA=2\sqrt3,\ PQ=2PA=4\sqrt3.$$

$$\text{Area}(\triangle PQB)=\frac12\cdot PQ\cdot(OB-OA)=\frac12\cdot4\sqrt3\cdot12=24\sqrt3.$$

Solutions · 1