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CBSE Class 10 Maths (Standard) 2022 · Paper 30/3/1 · Question 11(a)

Circles 4 marks Medium
In Figure 3, two circles with centres at O and O' of radii and respectively, touch each other internally at A. A chord AB of the bigger circle meets the smaller circle at C. Show that C bisects AB.
A O O' B C Figure 3
Two internally touching circles; chord AB of the big circle meets the small circle at C

Answer

Triangles AO'C and AOB are similar with ratio , so ; hence C bisects AB. Proved.

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