A smaller circle touches internally to a larger circle at A and passes through the centre of the larger circle. O is the centre of the larger circle and BA, OA are the diameters of the larger and smaller circles respectively. Chord AC intersects the smaller circle at a point D. If AC = 12 cm, then AD is:

4 cm

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6 cm

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5.6 cm

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Solution

The correct option is B 6 cm
$∠ A D O$ is a right angle (angle of semicircle)
Again when OD is perpendicular to the chord AC and OD passes through the centre of circle ABC, then it must bisect the chord AC at D.
$∴ A D = C D = 6 c m$

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The correct option is B 6 cm∠ADO is a right angle (angle of semicircle) Again when OD is perpendicular to the chord AC and OD passes through the centre of circle ABC, then it must bisect the chord AC at D. ∴AD=CD=6cm

The correct option is B 6 cm
$∠ A D O$ is a right angle (angle of semicircle)
Again when OD is perpendicular to the chord AC and OD passes through the centre of circle ABC, then it must bisect the chord AC at D.
$∴ A D = C D = 6 c m$