Two circles with centers A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.
Circles
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Question

Two circles with centers A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.

KnowledgeBoat · Accepted Answer

We know that, If two circles touch internally, then distance between their centres is equal to the difference of their radii. So, AB = (5 - 3) cm = 2 cm. Also, the common chord PQ is the perpendicular bisector of AB. Thus, AC = CB = = 1 cm. In right ∆ACP, we have ⇒ AP² = AC² + CP² [By pythagoras theorem] ⇒ 5² = 1² + CP² ⇒ CP² = 25 - 1 = 24 ⇒ CP = cm Now, PQ = 2 CP = 2 x cm ≈ 9.8 cm. Hence, the length of PQ is cm ≈ 9.8 cm.

Mathematics

Two circles with centers A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.

Circles

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