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Relation between Areas and Sides of Similar Triangles

35. If P is a...

Question

35. If P is a point inside a scalene triangle ABC such that triangle APB, triangle BPC and triangle CPA have the same area, then P must be (1) incentre of triangle ABC (2) circumcenter of triangle ABC (3) centroid of triangle ABC (4) orthocentre of triangle ABC

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Similar questions

P

A B C

Δ A P B

Δ B P C

Δ C P A

P

¯ ¯¯¯¯¯¯ ¯ Q P = 3 ¯ ¯¯¯¯¯¯¯ ¯ Q G

A (1, 0), B (6, 2)

C (\frac{3}{2}, 6)

A B C

P

A B C

A P C

A P B

B P C

P Q

Q

(- \frac{7}{6}, - \frac{1}{3})

In triangle ABC, D is a point on side BC such that 2BD = 3DC. Which of the following option is correct?

A B C

A B, B C

A C

P, Q

R

O

A B C,

I.

△ O B C

\frac{1}{2} \times B C \times radius of incircle

II.

A B + C Q = B Q + A C

III.

△ A B C

\frac{1}{2} \times perimeter of △ A B C \times radius of incircle

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