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March 29th, 2018, 01:00 AM   #1
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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.
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March 29th, 2018, 05:04 AM   #2
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2) 20
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March 29th, 2018, 07:31 AM   #3
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How? What procedure have you followed?
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March 29th, 2018, 08:35 AM   #4
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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 08:56 AM. Reason: added NOTE
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March 29th, 2018, 08:36 PM   #5
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Why should I pretend triangle ABC is isosceles?

Where did you get this numbers 20,35,125 etc?
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March 30th, 2018, 04:41 AM   #6
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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.
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April 1st, 2018, 08:46 AM   #7
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Ok, point P is outside the triangle, now please tell Why should I assume triangle is isosceles?
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April 1st, 2018, 08:55 AM   #8
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Just to get practice: it is easiest case.
SHOW your work if you want further help.
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April 1st, 2018, 09:06 AM   #9
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https://i.imgur.com/2fRbKn4r.jpg

This is how my triangle looks like.
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April 1st, 2018, 09:49 AM   #10
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Messy as hell, but basically correct!

Now, IF triangle ABC is isosceles:
angleABC = angleACB = ?
angleABP = ?
angleACP = ?
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