In the triangle ABC, the point P lies on the side AC such that angle BPC = angle ABC. Show that the triangles BPC and ABC are similar.

If AB = 4cm , Ac = 8cm , BP = 3cm , find the area of the triangle BPC.

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- Oct 9th 2008, 03:18 AMose90Deductive Geometry
In the triangle ABC, the point P lies on the side AC such that angle BPC = angle ABC. Show that the triangles BPC and ABC are similar.

If AB = 4cm , Ac = 8cm , BP = 3cm , find the area of the triangle BPC. - Oct 9th 2008, 04:13 AMose90
- Oct 9th 2008, 04:27 AMticbol
The part one is because the two said triangles have two angles equal each to each that's why they are similar.

For part two, use their similar properties.

AB /AC = BP /BC

BC = (8*3)/4 = 6

AB /BC = BP /PC

PC = (6*3)/4 = 4.5

You have now the 3 sides of triangle BPC.

Use the Heron's formula for the area. - Oct 9th 2008, 05:56 AMose90