Two circles of radii 8 cm and 3 cm have a direct common tangent of length 10 cm. Find the distance between their centres, up to two places of decimal.
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Question

Two circles of radii 8 cm and 3 cm have a direct common tangent of length 10 cm. Find the distance between their centres, up to two places of decimal.

KnowledgeBoat · Accepted Answer

Let there be two circles with centre A and B with radius 8 cm and 3 cm respectively. Let TT' be the length of common tangent. Construct a right-angled triangle Δ ADB by drawing a line from center B parallel to TT' to intersect radius AT at D. From figure, ⇒ TT' = BD = 10 cm ⇒ DT = BT' = 3 cm. ⇒ AD = AT - DT = 8 - 3 = 5 cm. In right angled triangle ADB, ⇒ AB2 = AD2 + DB2 ⇒ AB2 = 102 + 52 ⇒ AB2 = 100 + 25 ⇒ AB2 = 125 ⇒ AB = ⇒ AB = 11.18 cm. Hence, the distance between the centres 11.18 cm.

Mathematics

Two circles of radii 8 cm and 3 cm have a direct common tangent of length 10 cm. Find the distance between their centres, up to two places of decimal.

Circles

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