If `R_1` is the circumradius of the pedal triangle of a given triangle `A B C ,a n dR_2` is the circumradius of the pedal triangle of the pedal triangle formed, and so on `R_3,R_4` then the value of `sum_(i=1)^ooR_i ,` where `R` (circumradius) of` A B C` is `5` is 8 (b) 10 (c) 12 (d) 15

Options

A. 8
B. 10
C. 12
D. 15

Answer

B

Explanation

Circumradius of triangle ABC, R = 5
`:.` Circumradius of pedal triangle, `R_(1) = 5//2` and so on.
Now, `underset(i=1)overset(oo)sum R_(i) + R_(1) + R_(2) + R_(3) + ...oo`
`= 5 + (5)/(2) + (5)/(2^(2)) + ...oo`
`= 5.(5)/(1-(1)/(2)) = 10`