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Three circles touch each other externall...

Three circles touch each other externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 4. Then, the ratio of their product of radii to the sum of the radii is

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To solve the problem, we need to find the ratio of the product of the radii of three circles that touch each other externally to the sum of their radii. Let's denote the radii of the circles as \( r_1, r_2, \) and \( r_3 \). ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have three circles that touch each other externally. The tangents at the points of contact meet at a point, and the distance from this point to the point of contact is given as 4. 2. **Using Triangle Properties**: ...
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