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19/06/2021 11:55 am
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Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
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19/06/2021 11:59 am
From the above diagram, AB is tangent to the smaller circle to point P.
∴ OP ⊥ AB
Using Pythagoras theorem in triangle OPA,
OA2 = AP2 + OP2
52 = AP2 + 32
AP2 = 25 - 9
AP = 4
Now, as OP ⊥ AB,
Since the perpendicular from the center of the circle bisects the chord, AP will be equal to PB
So, AB = 2AP
= 2 × 4 = 8 cm
So, the length of the chord of the larger circle is 8 cm.