If ` A B C` is isosceles with `A B=A C` and `C(O ,\ r)` is the incircle of the ` A B C` touching `B C` at `L` , prove that `L` bisects `B C` .

If ABC is isosceles with AB=AC and C(O,r) is the incircle of the ABC touching BC at L, prove that L bisects BC .

In Figure, A B C is an isosceles triangle in which A B=A Cdot and C P||A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

In Figure, A B C is an isosceles triangle in which A B=A CdotC P A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

A B C is an isosceles triangle with A B=A C and D is a point on A C such that B C^2=A CXC D . Prove that B D=B C .

A B C is an isosceles triangle with A B=A C and D is a point on A C such that B C^2=A CxC Ddot Prove that B D=B C

If DeltaA B C is an isosceles triangle such that A B=A C ,\ then altitude A D from A on B C bisects B C (Fig.43).

A B C is an isosceles triangle with A C=B C . If A B^2=2\ A C^2 , prove that A B C is right triangle.