If `R_(1)` is the circumradius of the pedal triangle of a given triangle ABC, and `R_(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)^(oo) R_(i)`, where R (circumradius) of `DeltaABC` is 5 is

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`