`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 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)

In A B C , the bisector of /_B meets A C at Ddot A line P Q A C meets A B , B Ca n dB D at P ,Qa n dR respectively, Show that P RdotB Q=Q RdotB P (ii) A BxC Q=B CxA P

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

If a,b,c are in H.P.show that (a-b)/(b-c)=(a)/(c)

For any three events A,B and C, prove that,P(A uu B uu C)=P(A)+P(B)+P(C)-P(A nn B)-P(B nn C)-P(C nn A)+P(A nn B nn C)

If A o* B are two events then P{(A nnbar(B))uu(bar(A)nn B)}=(i)P(A uu B)-P(A nn B)(ii)P(A uu B)+P(A nn B)( iii) P(A)+P(B)(iv)P(A)+P(B)+P(A nn B)

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, 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)

In ABC,/_A=60^(@),/_B=80^(0) and the bisectors of /_B and /_C meet at O. Find : (i) /_C( ii) /_BOC .