Construct two chords of length 6 cm and 8 cm on the same 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 $4.5 c m$
Mark a chord of $6 c m$ and $8 c m$ on the same side of segment.
Let $M$ and $N$ be the midpoint of chord $C D$ and $A B$ respectively.
$O D$ and $O B$ are radius of circle
$(O M)^{2} = (O D)^{2} - (M D)^{2} O M = \sqrt{(4.5)^{2} - 4^{2}} = 2.062 (O N)^{2} = (O B)^{2} - (N B)^{2} O N = \sqrt{(4.5)^{2} - 3^{2}} = 3.354 M N = O N - O M M N = 3.354 - 2.062 M N = 1.292$

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Construct two chords of length 6 cm and 8 cm on the same 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 4.5cmMark a chord of 6cm and 8cm on the same side of segment.Let M and N be the midpoint of chord CD and AB respectively.OD and OB are radius of circle(OM)2=(OD)2−(MD)2OM=√(4.5)2−42=2.062(ON)2=(OB)2−(NB)2ON=√(4.5)2−32=3.354MN=ON−OMMN=3.354−2.062MN=1.292