Trollathon #1.5 : A Geometry

Geometry Level 4

Let ABC be a triangle. Let I be the incenter of ABC. Let D, E, F be the foot of altitudes from C to AB, B to AC and A to BC respectively. Let the circumcenter of ADE be O. Let ∠ B A I = 6 ∘ \angle BAI = 6^{\circ} . Let Q be the circumcenter of ABC. Find ∠ B Q C \angle BQC .


The answer is 24.

Zi Song Yeoh by Zi Song Yeoh , 20, Malaysia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Zi Song Yeoh
Apr 2, 2014

∠ B Q C = 2 ∠ B A C = 2 ( 2 ∠ B A I ) = 2 ( 2 ⋅ 6 ∘ ) = 24 ∘ \angle BQC = 2\angle BAC = 2(2 \angle BAI) = 2(2 \cdot 6^{\circ}) = \boxed{24}^{\circ}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

I can't believe I actually drew a diagram for this. -.-

Sreejato Bhattacharya - 7 years, 2 months ago

Log in to reply

hey me too. :(

敬全 钟 - 7 years, 2 months ago

I did the same but I failed

Mardokay Mosazghi - 7 years, 1 month ago

Wasn't a diagram necessary?

Kenny Lau - 6 years, 11 months ago

So easy!!! But still 80 points!!! Did the same!

Kartik Sharma - 6 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...