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Construct Triangle When Its Base, Difference of the Other Two Sides and One Base Angle Are Given

In a triangle...

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In a triangle ABC, angle ABC is of 45 , then prove that (AC)2 = (AB)2 + (BC)2 - 4area of triangle ABC.

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Q. In triangle ABC,

B C^{2}

A B^{2}

A C^{2}

, then __________ is a right angle

A B C

is a triangle in which

∠ A B C < 90^{o}

A D ⊥ B C .

A C^{2} = A B^{2} + B C^{2} - 2 B C . B D

.

In fig., $A B C$ is a triangle in which $∠ A B C > 90^{o}$ and $A D ⊥ C B$ produced. Prove that $A C^{2} = A B^{2} + B C^{2} + 2 B C . B D$ .

A B C

is a triangle in which

∠ A B C < 90^{\circ}

A D ⊥ B C .

A C^{2} = A B^{2} + B C^{2} - 2 B C . D B .

Q. In triangle ABC, if

A P ⊥ B C

A C^{2} = B C^{2} - A B^{2}

, then prove that

P A^{2} = P B \times C P

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