AB is the chord of the circle C--. With chord AB as the diameter, a semicircle is drawn inside the circle. Another chord CD is tangent to this semicircle and it is parallel to chord AB. If AB = 16 cm and CD = 8 cm, then find the radius of the circle.a)b)c)d)Correct answer is option 'B'. Can you explain this answer?

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AB is the chord of the circle C-|. With chord AB as the diameter, a semicircle is drawn inside the circle. Another chord CD is tangent to this semicircle and it is parallel to chord AB. If AB = 16 cm and CD = 8 cm, then find the radius of the circle.

Correct answer is option 'B'. Can you explain this answer?

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AB is the chord of the circle C-|. With chord AB as the diameter, a se...

Let O be the centre of the circle and the radius be R.
Also, let ON = x
OM = (8 - x)
Refer to the following diagram.

In ΔDNO, DN² + NO² = DO²...[By Pythagoras Theorem]
4² + x² = R² ...(i)
In ΔAMO, AM² + OM² = OA² ...[By Pythagoras Theorem] .
8² + (8 - x)² = R² ... (ii)
Solving equations (i) and (ii), we get,
x = 7 cm
Substituting the value of x in (ii), we get,

Hence, option 2.

Note: Considering AB and CD on the same side of the centre O gives a negative value of x, which indicates that AB and CD lie on opposite sides of the centre.

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