in a right angle triangle abc angle b is equal to 90 degree and D is the midpoint of the hypotenuse AC prove that AC is equals to 2 BD
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Step-by-step explanation:
GIVEN: A right triangle ABC, right angled at B. D is the mid point of AC, ie, AD = CD
TO PROVE : BD = AC/2
Since, circumcentre of any right triangle is the mid point of its hypotenuse.
=> D is the centre of the circle passing through A, B & C
=> AD = BD = CD ( being radii of the same circle)
Or 2AD = 2BD
=> AC = 2BD
=> BD = AC/2
here we can write it as AC=2BD
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