Mathematics
A chord of length 8 cm is drawn at a distance of 3 cm from the center of a circle. Calculate the radius of the circle.
Circles
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Answer
Let AB = 8 cm be the chord of the circle with center O.
We know that,
Perpendicular from center to chord, bisects the chord.
∴ AC = = 4 cm.
In right angled triangle OAC,
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ OA2 = OC2 + AC2
⇒ OA2 = 32 + 42
⇒ OA2 = 9 + 16
⇒ OA2 = 25
⇒ OA = = 5 cm.
Hence, radius of circle = 5 cm.
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