Question

∆ABC is an isosceles triangle in which AB=AC. A circle is drawn inside the triangle such that it touches AB at E and BC at D and AC at F. Show that D is mid- point of BC....

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

AF = AE(BTW THE WHOLE SUM IS BASED ON THE THEOREM THAT 2         TANGENTS DRAWN FROM AN EXTERNAL POINT TO A CIRCLE ARE EQUAL IN LENGTH)

WE KNOW THAT AB = AC

SO AB - AE = AC - AF

SO BE = CF

NOW,

BE = BD , CD = CF

SO BD = CD

SO D IS THE MIDPOINT OF BC

HENCE PROVED

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