Let p and q be the length of two chords of a circle which subtend angles 3 6 o and 6 0 o respectively at the centre of the circle. Then, the angle (in radian) subtended by the chord of length p + q at the centre of the circle is (use π = 3 . 1 )

Step-by-step solution

If l is the length of the chord, then l = 2 r s i n θ 2 . p = 2 r s i n  18 o ,   q = 2 r sin ⁡ 30 o ⇒ p + q = 2 r sin 18 o + sin ⁡ 30 o = 2 r 5 - 1 4 + 1 2 = 2 r 5 + 1 4 = 2 r c o s 36 o = 2 r s i n 54 o = 2 r s i n 108 o 2 ⇒ p + q subtends an angle 108 o at the centre 108 o = 1.86 radian