Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is
Explanation:
Let the radius of the third circle be ‘x’ cm.
AF = DE = 4 cm ⇒ AK = DC = (4 – x) cm In ∆ADC, AC2 = AD2 + DC2. (4 + x)2 = 42 + (4 – x)2 ∴ x = 1. Hence, option (a).
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