Prove that the midpoint of hypotenuse of right angle triangle is equidistant from three vertices

Asked by sachin0706 | 22nd Mar, 2009, 06:50: PM

Expert Answer:

Let P be the mid point of the hypo. of the right triangle ABC, right angled at B.

Draw a  line parallel to BC   from P meeting AB at D.

Join PB.

 in triangles,PAD and PBD,

angle PDA= angle PDB (90 each due to conv of  mid point theorem)

PD=PD(common)

AD=DB( as D is mid point of AB)

so triangles PAD  and PBD are congruent by SAS rule.

PA=PB(C.P.C.T.)

but

 PA=PC(given as P is mid point )

So,

 PA=PC=PB

Answered by  | 28th Nov, 2017, 02:51: PM