Question

in a triangle if the median ad is perpendicular to the BC then prove that triangle is an isosceles triangle.​

Answer 1

Proof:-

the perpendicular drawn from the centre of the circle to the chord bisects the chord

therefore BD=DC........,..................1)

In triangle ABD and triangle ACD

1) seg BD=seg CD........from 1)

2) seg AD=seg AD.........common side

3) angle ADB=angle ADC..Each angle is 90°

therefore∆ ABC=∆ACD

therefore seg AB= seg AC...c.s.c.t

therefore ∆ABC is an