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# The figure given below, shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4cm, find the radius of the circle. - ICSE Class 10 - Mathematics

ConceptChord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof)

#### Question

The figure given below, shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4cm, find the radius of the circle.

#### Solution

Let the radius of the circle be r cm.
∴ OE = OB- EB = r-4
Join OC
In right ΔOEC,
OC^2= OE^2+ CE^2
⇒ r ^2= (r-4)^2+(8)^2
⇒  r ^2 = r ^2-8r +16+64
⇒ 8r = 80
∴ r =10 cm
Hence, radius of the circle is 10 cm.

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Solution The figure given below, shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4cm, find the radius of the circle. Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof).
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