Question:
At one end of a dimeter AB of a circle of radius 5cm,tangents XAY is drawn to the circle.what is the length of the chord CD which is parallel to XY
Answer:
From the figure,
AM = 8 cm
and OM = AM - AO
=> OM = 8 - 5 = 3 xm
Since OM is perpendicular to the chord CD
So, in triangle OCM,
Apply Pythagorus Theorem,
CM2 + OM2 = OC2
=> CM2 + 32 = 52
=> CM2 + 9 = 25
=> CM2 = 25 - 9
=> CM2 = 16
=> CM = √16
=> CM = 4 cm
Now, CD = 2 * CM
=> CD = 2 * 4
=> CD = 8 cm
So, the length of the chord CD is 8 cm
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