If the length of a common external tangent to two circles is 9 and that of a common internal tangent is 5, then what is the product of the radii of the two circles?

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**Formula used:**
Length of external tangent = √(d² - (r1 - r2)²)
Length of internal tangent = √(d² - (r1 + r2)²)
Where d = distance between centres, r1 and r2 are the radii.
**Step 1:** Square both equations.
External tangent: 81 = d² - (r1 - r2)²
Internal tangent: 25 = d² - (r1 + r2)²
**Step 2:** Subtract the second equation from the first.
81 - 25 = (r1 + r2)² - (r1 - r2)²
56 = (r1² + 2r1r2 + r2²) - (r1² - 2r1r2 + r2²)
56 = 4r1r2
**Step 3:** Find the product of radii.
r1 × r2 = 56 / 4 = **14**
**The product of the radii of the two circles is 14.**

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