This applet explores the variation of the length of a certain segment in a triangle and asks when this length will be a minimum.
ABC is a triangle in which angle B and angle C are acute. P is a variable point on its base BC. From P, perpendiculars PQ and PR are drawn to sides AC and AB respectively. Segment QR is then drawn.
Where should point P be located on BC for QR to have minimum length?
The t-slider allows the user to drag P along BC, and the graph shows the variation of the length of QR.

What do you notice? For which position of P is the length of QR the least?