Make parallel lines of AB, BC and AC respectively through a point P in the triangle ABC Drawing

Make parallel lines of AB, BC and AC respectively through a point P in the triangle ABC Drawing

As shown in the figure:
 

As shown in the figure, it is known that in △ ABC, the bisector of ∠ C intersects AB at point D, and the parallel line of BC through D intersects AC at E. if AC = 6, BC = 12, the length of De is obtained

∵ CD bisects ∠ ACB, de ‖ BC, ∵ DCB = ∠ DCE = ∠ EDC. ∵ de = EC. ∵ de ‖ BC, ∵ ade ∵ ABC. ∵ DEBC = aeac. Let de = x, then de = EC = x, ∵ AC = 6, BC = 12, ∵ X12 = 6 − X6, ∵ x = 4, ∵ de = 4

In the triangle ABC, AB, AC are 3, BC are 2, the bisector of angle ABC intersects the parallel line of BC at D, find the area of triangle abd and write the process

The height of BC side of isosceles triangle ABC is 2 root sign 2, ad is parallel to BC and BD is angle bisector, so the angle abd = angle DBC = angle ADB, so ad = AB = 3, so the height of triangle ADB is 2 root sign 2, so the area of triangle abd is 3 times (2 root sign 2) and then divided by 2 = (3 root sign 2)