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Three Points on a Line

in triangle p...

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in triangle pqr angle qpr =angle pqr and m, n are points on sides qr and pr respectively such that qm= pn prove that op = o

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D

is a point on the side

Q R

P Q R

such that angles

P D R

Q P R

are equal. Prove that

Q R . D R = {P R}^{2} .

△ P Q R, P R^{2} - P Q^{2} = Q R^{2}

M

is a point on side

P R

Q M ⊥ P R

Q M^{2} = P M \times M R

S

T

are points on sides

P R

Q R

△ P Q R

∠ P = ∠ R T S

△ R P Q \sim △ R T S

.

△ P Q R, N

P R

Q N ⊥ P R

P N \times N R = {Q N}^{2}

∠ P Q R = 90^{\circ}

Q. In figure, the side

Q R

△ P Q R

is product to a point

S

. If the bisectors of

∠ P Q R

∠ P R S

T

, then prove that

∠ Q T R = \frac{1}{2} ∠ Q P R

.

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