Question

12. In the figure, the center of the circle is 0 and the diameter AB is equal to the chord (D at point E)
Claim. Also, if CE = ED = 8 cm and EB = 4 cm, the radius of the circle
A) 8 cm
B) 4 cm
C) 6 cm
D) 10 cm​

Answer 1

Answer:

Let the radius of a circle be x

So, OC=OD=x

As, OB=OE+EB

x=OE+4 [Since Ob is the radius and EB=4 cm given]

OE=x−4

We know that if a line drawn from the centre to the chord bisects the chord, then it is perpendicular to the chord

Hence, OE⊥CD

In △OED

OE2 +ED2 =OD2

(x−4)2 +8^2 =x2

x2+16−8x+64=x2

−8x+80=0

8x=80

x=10 cm

Thus, radius of the circle is 10 cm.

So the answer is D) 10 cm.

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