In the adjoining figure, two circles of radii $10 c m$ and $8 c m$ intersect each other at $P$ and $Q$ and the length of the common chord is $12 c m$ . Find the distance between their centres.

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Solution

$\begin{matrix} O P = O L = 8 c m O^{'} P = O^{'} L = 10 c m P θ = 12 c m R a d i u s d r a w n p e r p e n d i c u l a r t o c h o r d b i s e c t t h e c h o r d . ∴ O L^{2} = O P^{2} - P C^{2} = 64 - 36 ∴ O L = \sqrt{28} = 5.292 c m ∴ O^{'} L^{2} = O^{'} P^{2} - P L^{2} = 100 - 36 O^{'} L - \sqrt{64} = 8 c m . ∴ 00^{'} = O L + O^{'} L = 5.292 + 8 = 13.292 c m . \end{matrix}$

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In the adjoining figure, two circles of radii 10 cm and 8 cm intersect each other at P and Q and the length of the common chord is 12 cm. Find the distance between their centres.

OP=OL=8cmO′P=O′L=10cmPθ=12cmRadiusdrawnperpendiculartochordbisectthechord.∴OL2=OP2−PC2=64−36∴OL=√28=5.292cm∴O′L2=O′P2−PL2=100−36O′L−√64=8cm.∴00′=OL+O′L=5.292+8=13.292cm.

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