isi-entrance 2014 Q11

isi-entrance · India · solved Circles Inscribed/Circumscribed Circle Computations
A circle of radius $r$ is inscribed in a circular sector. The chord of the sector has length $a$. If the circle touches the chord and the two radii of the sector, find the relation between $a$ and $r$.
(A) $a = 8r/5$ (B) $a = 5r/8$ (C) $a = 4r/3$ (D) $a = 3r/4$
(D) $a = 8r/5$
A circle of radius $r$ is inscribed in a circular sector. The chord of the sector has length $a$. If the circle touches the chord and the two radii of the sector, find the relation between $a$ and $r$.

(A) $a = 8r/5$ \quad (B) $a = 5r/8$ \quad (C) $a = 4r/3$ \quad (D) $a = 3r/4$