The distance of the chord of length 16cm from the center of the circle of diameter 20cm is:

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3 cm

4 cm

5 cm

6 cm

answer is D.

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Detailed Solution

radius of the circle, OM = 20/2 = 10 cm
The chord AB is 16cm, half of the chord will be CB = 8 cm.
Consider the triangle OCB,
Since radius OM is equal to OB, then
OB = 10cm Question Image

{OB}^{2} = {OC}^{2} + {CB}^{2}

\Rightarrow 10^{2} = {OC}^{2} + 8^{2}

\Rightarrow {OC}^{2} = 100 - 64 = 36

\Rightarrow OC = 6

cm
Thus, the distance of the chord from the diameter is 6 cm.
So, Option 4 is correct.

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