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In the isosceles triangle ABC, AB=AC, if...

In the isosceles triangle `ABC, AB=AC,` if a circle is drawn with the side AB as diamter then the circle intersects the side BC at the point D. When BD=4 cm , find the the length of CD.

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Let O is the mid-point of AB. Circle drawn with centre at O intersect the side BC at the point D. Let us join A,D. then `angle ADB` is a semi-circular angle.
`:. angle ADB=90^(@), :. angle ADC=90^(@)`
Now, in `Delta ABD and Delta ACD` , we have `AB=AC angle ABD= angle ACD and angle ADB= a angle ADC`.
`:. Delta ABD ~= Delta ACD` [ by the A-A-S condition of congruency]
`:. Bd =CD [ :.` similar side os congruent triangle]
But BD= 4 cm (Given) ` :. CD=4 cm`
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