Question

In the figure, given alongside, CD is diameter which meets the chord AB at E, such that AE = BE = 4 cm. If CE is 3 cm, find the radius of the circle.

Answer 1

ans: 6.5 cm

solved in attachment

Answer 2

Radius = 4 cm

Explanation:

Given: CD is diameter which meets the chord AB at E, such that AE = BE = 4 cm. CE is 3 cm.

From the given information, we infer that the diameter CD bisects the chord AB. So CD is perpendicular to AB.

OC is the radius of the cirlce, r.

EC is 3 cm.

So OE will be (r - 4) cm.

In triangle OEB, OE = 3 cm and EB = 4cm. One angle is 90 degree.

So OB^2 = OE^2 + EB^2

r^2 = (r-4)^2 + 4^2

r^2 = r^2 + 16 -8r + 16

8r = 32

Therefore r = 32 / 8 = 4 cm