VTMO 2026 - Grade 7 - Semifinal - SET 6 - Self-study Question 16

Question 16

In triangle $ABC$, the external bisector at $B$ meets the internal bisector at $C$ at $D$, and the external bisector at $C$ meets the internal bisector at $B$ at $E$. Find the correct relation between the angle measures $p,q,r$ shown in the figure.

Question illustration

$q+2r=3p$
$2q+4r=5p$
$4q-r=2p$
$3q+2r=4p$
$r+3q=2p$