If the angle of intersection at a point where the two circles with radii 5 c m and 12 c m intersect is 90 ° , then the length (in cm) of their common chord is:

Question

If the angle of intersection at a point where the two circles with radii 5 c m and 12 c m intersect is 90 ° , then the length (in cm) of their common chord is:, 120 13, 60 13, 13 5, 13 2

MARKS App · Accepted Answer

∵ C 1 P = 5 C 2 P = 12 & ∠ C 1 P C 2 = 90 o ∴ C 1 C 2 = 13 ∴ Δ C C 2 P tan ⁡ θ = 12 5 ⇒ sin ⁡ θ = 12 13 C 1 C 2 biscets the P Q at R & C 1 C 2 ⊥ P Q in Δ P C 1 R , s i n θ = P R 5 ⇒ 12 13 = P R 5 ⇒ P R = 60 13 & P Q = 2 P R = 120 13

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