(ii) Prove : If two circles touch each other, their point of contact lies on the line
joining their centres.
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Given : two circles touch each other,
To Find : prove that their point of contact lies on the line joining their centers.
Solution:
Two circles touches each other at A
Center are x and y of each circle
Draw a tangent PA ( P is a point out side circle )
Hence ∠XAP = 90° and ∠ YAP = 90°
∠XAP + ∠ YAP = 90° + 90°
=>∠XAP + ∠ YAP = 180°
Hence XPY is a straight line
so point of contact lies on the line joining their centers.
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