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 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 ~= A C B , then A B C is isosceles with A B=A C (b) A B=B C A C=B C (d) Non e of t h e s e

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

In Figure, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles. Figure

In A B C , A L and C M are the perpendiculars from the vertices A and C to B C and A B respectively. If A L and C M intersect at O , prove that: (i) O M A O L C (ii) (O A)/(O C)=(O M)/(O L)

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)

In an isosceles triangle ABC, with AB = A C , the bisectors of B and C intersect each other at O. Join A to O. Show that : (i) O B = O C (ii) AO bisects A

Triangles A B C and +DBC are on the same base B C with A, D on opposite side of line B C , such that a r(_|_ A B C)=a r( D B C)dot Show that B C bisects A Ddot

In Figure, A B C D is a trapezium in which A B||C D . Prove that: a r( A O D)=a r( B O C)dot