CN-TST 2016 Problem 15

Test 3

In cyclic quadrilateral $ABCD$ , $AB>BC$ , $AD>DC$ , $I,J$ are the incenters of $\triangle ABC$ , $\triangle ADC$ respectively. The circle with diameter $AC$ meets segment $IB$ at $X$ , and the extension of $JD$ at $Y$ . Prove that if the four points $B,I,J,D$ are concyclic, then $X,Y$ are the reflections of each other across $AC$ .

Attachments:

Screen Shot 2016-03-25 at 12.59.05 pm.png

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Solutions

Similar problems