# In a ABC?, the sides AB and AC are produced to P and Q respectively. The bisectors of ? PBC and ? QCB intersect at a point O. Prove that ? BOC =90 Â° ? 1/2 ?A

Solution:  Let $\\\angle PBC=2x$   , $\\\angle QCB=2y$

$\because$  OB  ,OC bisects the $\\\angle PBC$ and  $\\\angle QCB$ respectively

$\therefore \angle OBP=\angle OBC=2X/2=X\\ \\ \Rightarrow \angle OCB=OCQ=2y/2=y \\ \\$

$\because in \bigtriangleup BOC,\\ \\ \Rightarrow x+y+\angle BOC=180 \\ \\\Rightarrow x+y=180-\angle BOC............(1)$

$\\\because \angle ABC+\angle PBC=180\\ \\ \angle ABC=180-2x\\ \\$

Similarly , $\\\angle ABC=180-2y\\ \\$

$\because$ In $\because \bigtriangleup ABC$ $\angle BAC+\angle ABC+\angle ACB=180^{\circ}$

$\\ x+y=90+(1/2)\angle A$

Now, $\\180-\angle BOC=90+(1/2)\angle A\\ \\\Rightarrow \angle BOC=90-(1/2)\angle A$

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
##### Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-