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A chord of length 8 cm is at a distance of 3 cm from the centre of the circle.

Calculate the radius of the circle.

Answer:

AB is the chord of a circle with center O

And radius OA and OM ⊥ AB

AB = 8 cm

OM = 3 cm

OM ⊥ AB

M is the mid-point of AB

AM = ½ AB = ½ × 8 = 4 cm.

Now in right ∆OAM

\begin{aligned} &\mathrm{OA}^{2}=\mathrm{OM}^{2}+\mathrm{AM}^{2}\\ &\text { (By Pythagoras Axiom) }\\ &=(3)^{2}+(4)^{2}=9+16=25\\ &=(5)^{2}\\ &\mathrm{OA}=5 \mathrm{cm} \end{aligned}

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