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In the circle, chord AB of length 12 cm is bisected by diameter CD at P, so that CP = 3 cm. Radius of the circle is:

In the circle, chord AB of length 12 cm is bisected by diameter CD at P, so that CP = 3 cm. Radius of the circle is. Chord Properties of a Circle, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

  1. 5.2 cm

  2. 6.5 cm

  3. 7.5 cm

  4. 8.3 cm

Circles

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Answer

In the circle, chord AB of length 12 cm is bisected by diameter CD at P, so that CP = 3 cm. Radius of the circle is. Chord Properties of a Circle, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Given,

Chord AB = 12 cm

CD bisects chord AB at P

AP = PB = 122\dfrac{12}{2} = 6 cm

CP = 3 cm

OC = OA = R

OP = OC - CP = R - 3

In triangle OPA,

Apply the Pythagorean Theorem :

OA2 = OP2 + AP2

R2 = (R - 3)2 + 62

R2 = R2 - 6R + 9 + 36

R2 = R2 - 6R + 45

6R = 45

R = 456\dfrac{45}{6} = 7.5 cm

Hence, option 3 is the correct option.

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