+0  
 
0
42
5
avatar+71 

Angle bisectors AX and BY of triangle ABC meet at a point I. Find angle C  in degrees, if angle AIB is 109 degrees. 
 

This is the (really bad) diagram. https://latex.artofproblemsolving.com/9/a/4/9a410e2228e9f2f01c8a6c8990c2ea3c9ebff2a0.png

 

Thank you so much!!!!!

 

Noori :) 

 Jun 9, 2020
 #1
avatar+916 
+2

It's not a bad diagram. AoPS folks do a good job writing Asymptope code.

 

If you'll be so kind as to provide the week and problem number?

 

Thanks!

 Jun 9, 2020
 #2
avatar+71 
+2

I agree the diagram is great, but the lighting on the problem is bad :). Sure, Week 7 Problem 7

 Jun 9, 2020
 #3
avatar+916 
+2

So AIB is 109 degrees. IAB + IBA + 109 = 180, so IAB + IBA = 180 -109 = 71.

 

AX and BY are angle bisectors so IAB = CAB/2, and IBA = CBA/2. (CAB + CBA)/2 = 71. 

 

Rearrange the last equation and you should be very close to your answer.

 

If you don't understand anything, feel free to ask!

hugomimihu  Jun 9, 2020
 #4
avatar+71 
+2

Thank you so much!!!!!!!!! I got it. :)

Noori  Jun 9, 2020
 #5
avatar+916 
+1

:)

 

Good job!

hugomimihu  Jun 9, 2020

28 Online Users

avatar
avatar
avatar
avatar