Quantitative Aptitude Question on Triangles, Circles & Quadrilaterals

Question

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

Answer 1

Solution

The correct answer is (D): $8.8$

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B
$AB = \sqrt{3^2+4^2} = 5$
$OT = \frac{3×4}{5} = \frac{12}{5}$
$OT = 2.4M$
In $ΔOTQ$
$OQ^2 = OT^2+TQ^2 ⇒ OQ^2-OT^2$
= $(5)^2-(2.4)^2$
= $19.24$
$⇒ TQ = \sqrt{19.24} ≈ 4.4$
$∴ PQ=2TQ = 8.8m$