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. - Mathematics

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Sum

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.

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Solution


Let the radius of the circle be r cm.
∴ OE = OB - EB = r - 4
Join OC.
In right ΔOEC,
OC2 = OE2 + CE2
⇒ r2 = ( r - 4 )2 + (8)
⇒ r2 = r2 - 8r + 16 + 64
⇒  8r = 80
∴ r = 10 cm
Hence, radius of the circle is 10 cm.

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Chapter 17: Circle - Exercise 17 (A) [Page 211]

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Selina Concise Mathematics Class 9 ICSE
Chapter 17 Circle
Exercise 17 (A) | Q 9 | Page 211

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