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Home / Geometry / In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC.

# In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC.

General enunciation: In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC.

Particular enunciation: In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. It is required prove that PB>PC.
Proof: PB is the bisector of ∠B.
∴∠PBC=½∠B
PC is the bisector of ∠C.
We know,
In a triangle the angle opposite the greater side is greater than the angle opposite the smaller side since AB>AC
∴ ∠ACB>∠ABC
⟹½∠ACB>½∠ABC
⟹∠PCB>∠PBC
⟹PB>PC
Therefore PB>PC.(Proved)

## If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.

If two triangles have the three sides of the one equal to the three sides ...