March 29th, 2018, 01:00 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 294 Thanks: 1  what is the measure of ∠BPC ?
In Triangle ABC, the internal bisector of $\angle ABC$ and the external bisector of $\angle ACB$ meet at P. If $\angle BAC$ = 40 what is the measure of $\angle BPC$? 1) 40 2) 20 3) 70 4) 35 5) None of these. Last edited by Ganesh Ujwal; March 29th, 2018 at 01:08 AM. 
March 29th, 2018, 05:04 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,764 Thanks: 860 
2) 20

March 29th, 2018, 07:31 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 294 Thanks: 1 
How? What procedure have you followed?

March 29th, 2018, 08:35 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,764 Thanks: 860 
Just analysis. Pretend triangle ABC is isosceles: then easily seen that triangle PBC = 2035125. So no need to continue... NOTE: I'm using "external bisector" as shown here: http://jwilson.coe.uga.edu/MATH7200/Sect4.2.html Last edited by Denis; March 29th, 2018 at 08:56 AM. Reason: added NOTE 
March 29th, 2018, 08:36 PM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 294 Thanks: 1 
Why should I pretend triangle ABC is isosceles? Where did you get this numbers 20,35,125 etc? 
March 30th, 2018, 04:41 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,764 Thanks: 860 
You obviously think point P is inside triangle ABC. IT IS NOT! Trying out on an isosceles triangle is simply to see what you can do: we have no idea where you're at... If you cannot get "20,35,125" on your own, then you need classroom help. 
April 1st, 2018, 08:46 AM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 294 Thanks: 1 
Ok, point P is outside the triangle, now please tell Why should I assume triangle is isosceles?

April 1st, 2018, 08:55 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,764 Thanks: 860 
Just to get practice: it is easiest case. SHOW your work if you want further help. 
April 1st, 2018, 09:06 AM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 294 Thanks: 1  
April 1st, 2018, 09:49 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,764 Thanks: 860 
Messy as hell, but basically correct! Now, IF triangle ABC is isosceles: angleABC = angleACB = ? angleABP = ? angleACP = ? 

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