Triangle ABC is right angled at A. The circle with centre A and radius AB cuts BC and AC internally at D and E respectively. If BD = 20 and DC = 16 then the length AC equals

Engineering

Mathematics

A Circle

Question

$6 \sqrt{26}$

$6 \sqrt{21}$

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b² + r² = (36)² ....(1)
Also CD · CB = CE · CX (using power of the point C)
16 · 36 = (b – r)(b + r)
∴ b² – r² = 16 · 36

from (1) and (2)
2b² = 36(36 + 16) = 36 · 52
b² = 36 · 26 ⟹ b = $6 \sqrt{26}$

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