Question

two concentric circles of radius 15,12cm drawn length of chord of larger circle which touches smaller circle ​

Answer 1

here AC is radius of large circle 15 cm

AB is radius of small circle 12cm

and ABC is right angled triangle by theorem

by Pythagoras theorem

H²=P²+B²

15²= 12²+B²

B² = 15² -12² = 225-144 = 81

B= √81 = 9 cm

chord of large circle touches the smaller circle = 2×9 = 18 cm

Answer 2

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Let C1 and C2 be two circles of r = 15, 12

Let R1 = 15 cm

R2 = 12cm

Draw a chord AB tangent to C2 at point P.

Join O-A and O-B

OP = 12cm.....(Radius of smaller circle)

OA = OB = 15cm.......(Radius of bigger circle)

AB is tangent to C2 and OP perpendicular AB.

Angle OPA = Angle OPB = 90°

Using Pythagoras theorem

OA² = OP² + AP²

» AP² = OA²- OP²

» AP² = 15² - 12²

» AP² = 225 - 144

» AP² = 81

» AP = 9cm

Similarly PB = 5cm

» AB = AP + PB

» AB = 9 + 9

»AB = 18

Answer = 18