The chord RS of length 8 cm , of a circle with center C,cuts one of the
diameter PQ in a point T such that CT=TQ, If RT = 6,then the diameter of
the circle is
(a) 14 cm
(b) 8 cm
(c) 16 cm
(d) None of these
Let radius of the circle be r
PT = 3r/2 and TQ = r/2.
(3r/2) (r/2) = 6 x 2 = 12.
3r2/4 = 12
⇒ r2 = 16.
r = + 4.
Hence the diameter of the circle is 8 cm. But it is impossible to draw a chord of length 8 cm (other than the diameter) in a circle of diameter 8 cm. The circle must be imaginary.