Answer the following

Asked by tultuldutta58 | 8th Jan, 2018, 03:03: AM

Expert Answer:

 
begin mathsize 16px style In space triangle space ACD comma space DP space is space the space bisector space of space angle ADC.
rightwards double arrow AD over DC equals AP over PC space space space space space space.... left parenthesis straight i right parenthesis
In space triangle space ABC comma space BP space is space the space bisector space of space angle ABC.
rightwards double arrow AB over BC equals AP over PC space space space space space space.... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma
AD over DC equals AB over BC
rightwards double arrow AB over AD equals BC over DC space space space space.... left parenthesis iii right parenthesis
In space triangle space ABD comma space AQ space is space the space bisector space of space angle BAD.
rightwards double arrow AB over AD equals BQ over DQ space space space space.... left parenthesis iv right parenthesis
From space left parenthesis iii right parenthesis space and space left parenthesis iv right parenthesis
BC over DC equals BQ over DQ space space
Thus comma space in space triangle space CBD comma space straight Q space divides space BD space in space the space ratio space CB colon CD.
rightwards double arrow CQ thin space is space the space bisector space of space angle BCD.
Thus comma space bisectors space of space angle BAD space and space angle BCD space meet space on space the space diagonal space BD. end style

Answered by Rashmi Khot | 10th Jan, 2018, 09:00: AM