Let AD be the altitude of a triangle ABC. If (AB + AC) = p, (AB – AC) = q and (BD – CD) = r, then what is BC equal to?
- A. \frac{qr}{p}
- B. \frac{pr}{q}
- C. \frac{pq}{r} ✓
- D. p + q - r
Correct Answer: C. \frac{pq}{r}
Explanation
In right triangles ABD and ACD, AD^2 = AB^2 - BD^2 = AC^2 - CD^2. Rearranging gives AB^2 - AC^2 = BD^2 - CD^2, which factors to (AB + AC)(AB - AC) = (BD + CD)(BD - CD). Substituting the given values: pq = BC \times r, which gives BC = \frac{pq}{r}.
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