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Midpoints of two sides passing through a point

Source: NMTC 2019 junior P1

November 2, 2019

geometry

Problem Statement

In a convex quadrilateral

PQRS

, the areas of triangles

PQS

,

QRS

and

B

are in the ratio

3:4:1

. A line through

Q

cuts

PR

at

A

and

RS

at

B

such that

PA:PR=RB:RS

. Prove that

A

is the midpoint of

PR

and

B

is the midpoint of

RS

.

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