Mathematics
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?
Circles
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Answer
In the figure below, AB is the diameter and AC as the chord.
Now, draw OL ⊥ AC
Since, O is the centre of the circle and OL ⊥ AC.
∴ L bisects AC.
∴ AL = 6 cm and OA = radius = 10 cm.
Now, in right ∆OLA
⇒ OA2 = AL2 + OL2 [By Pythagoras Theorem]
⇒ 102 = 62 + OL2
⇒ OL2 = 100 - 36
⇒ OL2 = 64
⇒ OL = = 8 cm.
Hence, the chord is at a distance of 8 cm from the centre of the circle.
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