A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.
Let AB be the chord and O be the centre of the circle.
Let OC be the perpendicular drawn from O to AB.
We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.
∴ AB = 8 cm
⟹ AC = CB =`("AB")/2`
⟹ AC = CB =`8/2`
⟹ AC = CB = 4 cm
OA2 = OC2 + AC2 (By Pythagoras theorem)
⟹ OA2 = (4)2 + (3)2 = 25
⟹ OA = 5 cm
Hence, radius of the circle is 5 cm.
Video Tutorials For All Subjects
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