JEE PYQ: Circle Question 12
Question 12 - 2021 (26 Feb Shift 1)
In the circle given below, let $OA = 1$ unit, $OB = 13$ unit and $PQ \perp OB$. Then, the area of the triangle PQB (in square units) is:
(1) $26\sqrt{3}$
(2) $24\sqrt{2}$
(3) $24\sqrt{3}$
(4) $26\sqrt{2}$
Show Answer
Answer: (3)
Solution
$OA = 1$, $OB = 13$. Diameter $= 14$, so center $C$ at midpoint, $OC = 6.5$. $AC = 5.5$. $PA = \sqrt{6.5^2 - 5.5^2} = \sqrt{12}$. $PQ = 2\sqrt{12}$. Area $= \frac{1}{2} \times 2\sqrt{12} \times 12 = 12\sqrt{12} = 24\sqrt{3}$.
BETA
