In the picture, a circle is drawn with a line as diameter and a smaller circle with half the line as to diameter. Prove that any chord of the larger circle through the point where the circles meet is bisected by the small circle. Circles







4) In the picture, a circle is drawn with a line as diameter and a smaller circle with half the line as to diameter. Prove that any chord of the larger circle through the point where the circles meet is bisected by the small circle.


Answer :





∠A is common to both the triangles.


AO �1 = BO1 (the radii of the big circle)


∠ACO1 = ∠ADB = 90°


Hence,


in ΔACO1∼ ΔADB,


⇒ 


Since, the ratio is always equal, we can say that any chord of the larger circle through the point where the circles meet is bisected by the small circle.







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