CDS 2026 · PYQ · Geometry / Right Triangle · medium
ABC is a triangle right-angled at B. Points M and N trisect BC. If AM = 6 cm and AN = 9 cm, then what is AC equal to?
- A.4√39 cm
- B.2√39 cm✓ Correct
- C.24 cm
- D.20 cm
Let BC = 3k, so BM = k, BN = 2k. Let AB = c. Then AM² = c² + k² = 36 and AN² = c² + 4k² = 81. Subtracting: 3k² = 45, so k² = 15. Then c² = 36 − 15 = 21. BC = 3k, so BC² = 9k² = 135. Therefore AC² = c² + BC² = 21 + 135 = 156. AC = √156 = 2√39 cm.
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