Question

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

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Answer 1

Given that AP = 8 cm, BQ = 3 cm, AB = 10 cm

Draw QR $\perp$ to AP

ARQB forms a rectangle

AR = BQ = 3 cm

QR = AB = 10 cm.

RP = AP – AR

RP = 8 – 3 = 5 cm.

Applying Pythagoras theorem to ΔPQR

${PQ}^2$ = ${PR}^2$ + ${RQ}^2$

${PQ}^2$ = $5^2$ + ${10}^2$

${PQ}^2$ = 25 + 100

${PQ}^2$ = 125

PQ = 11.18 cm

Therefore the distance between the centers of the two circles is 11.18 cm