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 March 29th, 2018, 02:00 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 342 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 02:08 AM.
 March 29th, 2018, 06:04 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,444 Thanks: 946 2) 20
 March 29th, 2018, 08:31 AM #3 Senior Member   Joined: Aug 2014 From: India Posts: 342 Thanks: 1 How? What procedure have you followed?
 March 29th, 2018, 09:35 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,444 Thanks: 946 Just analysis. Pretend triangle ABC is isosceles: then easily seen that triangle PBC = 20-35-125. 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 09:56 AM. Reason: added NOTE
 March 29th, 2018, 09:36 PM #5 Senior Member   Joined: Aug 2014 From: India Posts: 342 Thanks: 1 Why should I pretend triangle ABC is isosceles? Where did you get this numbers 20,35,125 etc?
 March 30th, 2018, 05:41 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,444 Thanks: 946 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, 09:46 AM #7 Senior Member   Joined: Aug 2014 From: India Posts: 342 Thanks: 1 Ok, point P is outside the triangle, now please tell Why should I assume triangle is isosceles?
 April 1st, 2018, 09:55 AM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,444 Thanks: 946 Just to get practice: it is easiest case. SHOW your work if you want further help.
 April 1st, 2018, 10:06 AM #9 Senior Member   Joined: Aug 2014 From: India Posts: 342 Thanks: 1 https://i.imgur.com/2fRbKn4r.jpg This is how my triangle looks like.
 April 1st, 2018, 10:49 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,444 Thanks: 946 Messy as hell, but basically correct! Now, IF triangle ABC is isosceles: angleABC = angleACB = ? angleABP = ? angleACP = ?

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