Mathematics
The figure, given below, shows a circle with center O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, find the radius of the circle.
Circles
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Answer
Join OD.
Let radius of circle be x cm.
From figure,
Radius = OB = OD = x cm
⇒ OE = OB - EB = (x - 4) cm.
We know that,
A straight line drawn from the center of a circle to bisect a chord, is perpendicular to the chord.
∴ OE ⊥ CD
In right-angled triangle OED,
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ OD2 = OE2 + ED2
⇒ x2 = (x - 4)2 + 82
⇒ x2 = x2 + 42 - 2 × x × 4 + 64
⇒ x2 = x2 + 16 - 8x + 64
⇒ x2 - x2 + 8x = 80
⇒ 8x = 80
⇒ x = = 10 cm.
Hence, radius of circle = 10 cm.
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