`B O` and `C O` are respectively the bisectors of `/_B` and `/_C` of ` A B C` . `A O` produced meets `B C` at `P` . Show that: `(A B)/(B P)=(A O)/(O P)` (ii) `(A C)/(C P)=(A O)/(O P)` (iii) `(A B)/(A C)=(B P)/(P C)` (iv) `A P` is the bisector of `/_B A C` .

In a A B C , it is given that A B=A C and the bisectors of /_B and /_C intersect at O , If M is a point on B O produced, prove that /_M O C=/_A B Cdot

In a triangle A B C , the internal bisectors of /_B\ a n d\ /_C meet at P and the external bisectors of /_B\ a n d\ /_C meet at Q . Prove that /_B P C+\ /_B Q C=180^0

The sides A B and A C of A B C are product to P and Q\ respectively. the bisectors of exterior angles at B and C of A B C meet at O\ (fig.19) prove that /_B O C=90^0-1/2/_A

In a A B C , it is given that A B=A C and the bisectors of /_B\ a n d\ C intersect at Odot If M is a point on B O produced, prove that /_M O C=\ /_A B C

The sides A B and A C of a A B C are produced to P and Q respectively. If the bisectors of /_P B C AND /_Q C B intersect at O , then /_boc=90^0-1/2/_A GIVEN : A A B C in which sides A B and A C are produced to P and Q respectively. The bisectors of /_P B C and /_Q C B intersect at Odot

In figure, A B\ a n d\ C D are straight lines and O P\ a n d\ O Q are respectively the bisectors of angles /_B O D\ a n d\ /_A O C . Show that the rays O P\ a n d\ O Q are in the same line.

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A B in D ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

In A B C , /_A=60^0,\ /_B=80^0 and the bisectors of /_B\ a n d\ /_C meet at O . Find : (i) /_C (ii) /_B O Cdot

In Figure, P is a point in the interior of a parallelogram A B C D . Show that a r( A P B)+a r( P C D)=1/2a r(^(gm)A B C D) a R(A P D)+a r( P B C)=a r( A P B)+a r( P C D)

A B C D is a tetrahedron and O is any point. If the lines joining O to the vertices meet the opposite faces at P ,Q ,Ra n dS , prove that (O P)/(A P)+(O Q)/(B Q)+(O R)/(C R)+(O S)/(D S)=1.