Answer :

i) We know that,

In any triangle, line drawn parallel to one side, passing through mid-point of another side will also meet the third side at its mid-point.


Let AD be ‘x’, then DC = x. similarly AE = y then EB = y

By pythagorus theorem for bigger triangle ABC,


Similarly for smaller triangle AED,


From 1 & 2, we have

Hence proved.


We have the above following data.

And from pythagorous theorem,

We have

Hence the distance between mid-point of hypotenuse to vertex B (or) A (or) C is x

Hence proved.

iii) We know that

circumcentre is a point from which all the vertices are at equal distances.

In the above case, we have proved the mid-point of hypotenuse is equidistant from all the three vertices. Therefore mid-point of hypotenuse is the circumcentre of the given triangle.

Hence proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

In the picture beKerala Board Mathematics Part-1

AB and CD are parKerala Board Mathematics Part-1

In □ABC, the lineKerala Board Mathematics Part-1

In the parallelogKerala Board Mathematics Part-1

Prove that the quKerala Board Mathematics Part-1

Draw a right triaKerala Board Mathematics Part-1

In the picture, tKerala Board Mathematics Part-1