Two circles of radii 7 cm and 9 cm intersect at the points A and B. If AB = 6 cm and the distance between the centers of the circles is x cm, then the value of x (to the closest integer) is?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 15
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Concept |
Understanding |
Application |
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When 2 circles intersect each other, the shortest distance between them is perpendicular on the intersecting line and also bisects it. |
Given: AP = 7 cm and AQ = 9 cm AO = OB = AB/2 = 3 cm
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In triangle AOP: Applying Pythagoras theorem; OP2 = AP2 – AO2 ⇒ OP2 = 72 – 32 = 40 ⇒ OP = 6.32 cm (approx.) Similarly, in triangle AOQ: OQ2 = AQ2 – AO2 ⇒ OQ2 = 92 – 32 = 72 ⇒ OP = 8.48 cm (approx.) Hence, PQ = 6.32 + 8.48 = 14.8 ≈ 15 cm |