Question

if d is midpoint on hypotenuse bc of triangle abc . prove that ad = 1/2 bc​

Answer 1

Step-by-step explanation:

Right triangle ABC , right angled at A.

And D is the mid point of hypotenuse BC.

Since, mid point of the hypotenuse is circum centre of the right triangle. So ‘D' is the circumcentre of the right triangle ABC.

Hence AD, BD & CD become the radii of the circumcircle. ( as circum circle passes through the vertices of the right triangle)..

So, AD = BD = CD

But BD + CD = BC

SO, BD = CD = BC/2

Hence, AD = BC /2

Answer 2

Step-by-step explanation:

AD is half of AC,

As AC is the hypotenuse and has the largest length among all the sides of the right angled triangle.

Therefore AC is not equal to BC

and hence 1/2AC=AD cannot be half of BC

Therefore, AD is not equal to 1/2BC

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