Math CentralQuandaries & Queries


Question from mark, a student:

Three circles of radii 24 cm, 32 cm, and 42 cm are externally tangent to each other (each is tangent to the other two). Draw a diagram and using the Law of Cosines find the largest angle of the triangle formed by joining their centres.

Hi Mark,

I drew two circles with centres $A$ and $B$ that are tangent to each other at the point $P.$


I joined $A$ and $B$ to $P$ and drew the common tangent line $ST.$ Since $AP$ is a radius of the small circle and $PT$ is tangent to the circle, the angle $APT$ is a right angle. Similarly the angle $TPB$ is a right angle. Thus $AB$ is a straight line.

This is the key to your problem. See if you an solve the problem and write back if you need more assistance.


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