In a circle with centre P,the length of a dia | vedclass

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(B) Given that the diameter of the circle is $20 \, cm$,the radius $r = \frac{20}{2} = 10 \, cm$.Let $M$ be the midpoint of the chord $AB$ such that $

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$16$

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(B) Given that the diameter of the circle is $20 \, cm$,the radius $r = \frac{20}{2} = 10 \, cm$.Let $M$ be the midpoint of the chord $AB$ such that $PM \perp AB$. The distance from the centre $P$ to the chord $AB$ is $PM = 6 \, cm$.In the right-angled triangle $	riangle PMA$,by the Pythagorean theorem:$PA^2 = PM^2 + AM^2$$10^2 = 6^2 + AM^2$$100 = 36 + AM^2$$AM^2 = 100 - 36 = 64$$AM = \sqrt{64} = 8 \, cm$.Since the perpendicular from the centre to a chord bisects the chord,$AB = 2 	imes AM = 2 	imes 8 = 16 \, cm$.

In a circle with centre $P$,the length of a diameter is $20 \, cm$ and $AB$ is a chord of a circle at a distance $6 \, cm$ from the centre,then $AB = $ ........ $cm$.

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