pr is tangent to a circle at point p . q is another point on circle such that pq is diameter of circle and rq cuts circle at m . if radius of circle is 4 units and pr = 6 units . find ratio of triangle pmr to pqr .
let pm = y qm = x mr = 10 - x in triangle pqm , pm ^ 2 + qm ^ 2 = pq ^ 2 = > x ^ 2 + y ^ 2 = 64 . . . . . ( 1 ) in triangle pmr , pm ^ 2 + mr ^ 2 = pr ^ 2 y ^ 2 + ( 10 - x ) ^ 2 = 36 . . . . . . ( 2 ) solving for x and y x = 6.4 y = 4.8 taking permineter of triangle pqr = 24 perimeter of triangle pmr = 14.4 take ratio 14.4 / 24 = 0.6 answer : c
divide(triangle_perimeter(6, divide(multiply(multiply(4, const_2), 6), sqrt(add(power(multiply(4, const_2), const_2), power(6, const_2)))), divide(multiply(6, 6), multiply(4, const_2))), triangle_perimeter(multiply(4, const_2), 6, sqrt(add(power(multiply(4, const_2), const_2), power(6, const_2)))))