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The length of the direct common tangent to two circles of radii 12 cm and 4 cm is 15 cm. Calculate the distance between their centres.

Circles

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Answer

Let there be two circles with center A and B and radius 12 and 4 cm respectively.

From figure,

The length of the direct common tangent to two circles of radii 12 cm and 4 cm is 15 cm. Calculate the distance between their centres. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

TT' is the common tangent.

DT = BT' = 4 cm.

DB = TT' = 15 cm.

In right angled triangle ADB

AD = AT - DT = 12 - 4 = 8 cm

AB2=AD2+DB2AB2=82+152AB2=64+225AB2=289AB=289AB=17 cm.AB^2 = AD^2 + DB^2 \\[1em] AB^2 = 8^2 + 15^2 \\[1em] AB^2 = 64 + 225 \\[1em] AB^2 = 289 \\[1em] AB = \sqrt{289} \\[1em] AB = 17 \text{ cm}.

Hence, the distance between two centres = 17 cm.

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