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
Explanation:
The following figure can be drawn from the information given in the question.
In right triangle AOB, AB = 5 (Pythagorean triplet)
Also, OM is the altitude = 3×45 = 2.4
In right triangle OMP,
OP2 = OM2 + MP2
⇒ 52 + (2.4)2 + MP2
⇒ MP = 19.24
⇒ PQ = 2MP = 2 × 19.24 ≈ 2 × 4.4 = 8.8.
Hence, option (a).
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