Construct two chords of length 6.5 cm each on either side of the centre of a circle of radius 4.5 cm. Measure the distance between the centre and the chords.

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Solution

Draw a circle of radius $r = 4.5 c m$
Make a chord $A B$ of length $6.5 c m$
Let $M$ be the midpoint of $A B$ and $O M$ is the perpendicular bisector.
In $△ B O M$
$(O M)^{2} = (O B)^{2} - (M B)^{2} (O M)^{2} = (4.5)^{2} - (3.25)^{2} O M = \sqrt{9.6875} O M = 3.1125$
Since $C D = A B O N = O M = 3.1125$

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Construct two chords of length 6.5 cm each on either side of the centre of a circle of radius 4.5 cm. Measure the distance between the centre and the chords.

Draw a circle of radius r=4.5cmMake a chord AB of length 6.5cmLet M be the midpoint of AB and OM is the perpendicular bisector.In △BOM(OM)2=(OB)2−(MB)2(OM)2=(4.5)2−(3.25)2OM=√9.6875OM=3.1125Since CD=ABON=OM=3.1125