MathDB

25

Part of 2009 National Olympiad First Round

Problems(1)

Incircle touch

Source: 0

4/28/2009
The incircle of △ABC \triangle ABC touches BC BC, AC AC, and AB AB at A1 A_1, B1 B_1, and C1 C_1, respectively. The line AA1 AA_1 intersects the incircle at Q Q, again. A1C1 A_1C_1 and A1B1 A_1B_1 intersect the line, passing through A A and parallel to BC BC, at P P and R R, respectively. If \angle PQC_1 \equal{} 45^\circ and \angle RQB_1 \equal{} 65^\circ, then ∠PQR \angle PQR will be ?
<spanclass=′latex−bold′>(A)</span> 110∘<spanclass=′latex−bold′>(B)</span> 115∘<spanclass=′latex−bold′>(C)</span> 120∘<spanclass=′latex−bold′>(D)</span> 125∘<spanclass=′latex−bold′>(E)</span> 130∘<span class='latex-bold'>(A)</span>\ 110^\circ \qquad<span class='latex-bold'>(B)</span>\ 115^\circ \qquad<span class='latex-bold'>(C)</span>\ 120^\circ \qquad<span class='latex-bold'>(D)</span>\ 125^\circ \qquad<span class='latex-bold'>(E)</span>\ 130^\circ
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