IKMC 2027 - Grades 7-8 - Self-study SET 8 - Thematic Batch 3 Question 15

Question 15

Triangle ABC is right-angled at A, with AB=c, AX=p and XC=q as shown. Jenny and Vicky move at equal speeds in opposite directions, starting simultaneously at X and meeting at B. Express q in terms of p and c.

Editorial interpretation: The two routes follow the triangle boundary in opposite directions from X.

Question illustration

$\frac p2+c$
$\frac{pc}{2p+c}$
$\sqrt{p^2+c^2}+\frac c2$
$\frac{p+c}{2}$
$c-p$