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At point A on the diameter AB of a circle of radius $10$ cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of $16$ cm from A.
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AP = $16$ cm
$\therefore OP = 16 - 10 = 6$ cm
XY $||$ CD
$\therefore \angle CPO = 90^\circ$
In right $\triangle OPC$,
$CP = \sqrt{(10)^2 - (6)^2} = 8$ cm
CD = $2 \times CP$
$= 2 \times 8 = 16$ cm
$\therefore OP = 16 - 10 = 6$ cm
XY $||$ CD
$\therefore \angle CPO = 90^\circ$
In right $\triangle OPC$,
$CP = \sqrt{(10)^2 - (6)^2} = 8$ cm
CD = $2 \times CP$
$= 2 \times 8 = 16$ cm