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Question
In the figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is
Options
8 cm
4 cm
6 cm
10 cm
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Solution
10 cm
Explanation;
Hint:
Let the radius OD be x.
OE = OB – BE
= x – 4 ...(OB radius of the circle)
In the ΔOED,
OD2 = OE2 + ED2
x2 = (x – 4)2 + 82
x2 = x2 + 16 – 8x + 64
8x = 80
x = `80/8`
= 10 cm
Radius of the circle = 10 cm.
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