Q. 24.3( 11 Votes )

In Fig. 10.3, if

Answer :

Given:

Radius of the circle = r = AO = 5 cm


Length of chord AB = 8 cm


Since the line drawn through the center of a circle to bisect a chord is perpendicular to the chord, therefore AOC is a right angled triangle with C as the bisector of AB.


AC = 1/2(AB) = 8/2 = 4 cm


In right angled triangle AOC, by Pythagoras theorem, we have:


(AO)2 = (OC)2 + (AC)2


(5)2 = (OC)2 + (4)2


(OC)2 = (5)2 - (4)2


(OC)2 = 25 – 16


(OC)2 = 9


Take square root on both sides:


(OC) = 3


The distance of AC from the center of the circle is 3 cm.


Now, OD is the radius of the circle, OD = 5 cm


CD = OD – OC


CD = 5 – 3


CD = 2


CD = 2 cm

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