1. ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point intersects AB at P. Then AP : AB is :
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By: anil on 05 May 2019 01.57 am
Here, AM is tangent to the circle and APB is secant to the circle. Thus by tangent theorem : => $$AM^2 = AP imes AB$$ Also, $$AM = frac{AC}{2} = frac{AB}{2}$$ => $$(frac{AB}{2})^2 = AP imes AB$$ => $$frac{AP}{AB} = frac{1}{4}$$ => Required ratio = 1 : 4
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