Hello, bakchormee!

a) In one of your worst nightmares you are a contestant on a TV game show

that is designed to make you look silly. You and two other contestants have been

placed at the mid-points of the edges of a triangle. Each contestant has a pet flea

that is sitting on the opposing vertex. These are specially trained homing fleas;

once released from their vertex prisons they will travel in a straight line to their owners.

The winner is the person who is first re-united with their pet flea. The triangle has

sides of length 6, 9 and 11 metres and the pet fleas are in top shape having been

recently measured (with a flea-radar gun) to run at a staggering 0.666 m/sec.

You are on the side of length 9 metres. . All 3 fleas are released at the same time.

Are you a winner?

No, the winner is the person at the midpoint of 11-meter side.

. . [[The longest side is closest to its opposite vertex.]

(b) The fleas have been equipped with special little boots that leave a distinct trail

as they run home (to you). .Thus each flea draws a line over the triangle.

What interesting fact can you deduce about the three lines drawn by the fleas?

The fleas run along theof the triangle.medians

Hence, their paths intersect at a single point, the centroid

. . (center of gravity) of the triangle.