The diameter and a chord of circle have a common end-point. If the length of the diameter is 20 cm and the length of the chord is 12 cm, how far is the chord from the center of the circle?
The diameter and a chord of circle have a common end-point. If the length of the diameter is 20 cm and the length of the chord is 12 cm, how far is the chord from the center of the circle?

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(C) - 5

We have,

    \[AB\]

as the diameter and

    \[AC\]

as the chord.

Now, draw 

    \[OL\bot AC\]

Since

    \[OL\bot AC\]

 and hence it bisects

    \[AC\]

    \[O\]

is the centre of the circle.

Therefore,

    \[OA\text{ }=\text{ }10\text{ }cm\text{ }and\text{ }AL\text{ }=\text{ }6\text{ }cm\]

Now, in right

    \[\vartriangle OLA\]

    \[A{{O}^{2}}~=\text{ }A{{L}^{2~}}+\text{ }O{{L}^{2}}~\]

[By Pythagoras Theorem]

    \[{{10}^{2}}~=\text{ }{{6}^{2}}~+\text{ }O{{L}^{2}}\]

    \[O{{L}^{2}}~=\text{ }100\text{ }-\text{ }36\text{ }=\text{ }64\]

So,

    \[OL\text{ }=\text{ }8\text{ }cm\]

Therefore, the chord is at a distance of 8 cm from the centre of the circle.