# D is the mid point of side bc of an isosceles triangle abc with ab=ac. prove that the circle drawn with either of the equal side as a diameter passes through the point d

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by shubham

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by shubham

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ABC is an isosceles triangle

so ab=ac

d is the midpoint of BC

construct the circle and let side ab be its diameter

let another point g other than d pass through the circle(assumed)

construct AG

so angle AGB=90' (diameter property)

so AG is perpendicular to seg BC

therefor AG divides side BC(ABC is isosceles and isosceles triangle property)

so g is midpoint of seg BC

but d is midpoint of seg BC(given)

so d and g are one and the same

so point d passes through the circle drawn keeping ab as the diameter

similarly it can be proved for the other side also