Question

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

Answer 1

it is given that the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°.

we have to find the length of their common chord

let C₁ and C₂ are two circles of radius 5cm and 12cm respectively. point of intersection of circles is A and B as shown in figure.

here AB is common chord.

AC₁C₂ is a right angle triangle.

tanθ = 12/5 so, sinθ = 12/13

here C₁C₂ is perpendicular bisector of AB

so, AD = AB/2

then, sinθ = AD/AC₁ = (AB/2)/5

⇒12/13 = AB/10

⇒AB = 120/13

hence length of common chord is 120/13 cm