Triangle PQR and triangle OMR are two equilateral triangles such that M is the mid point of PR. If OQ intersects PR at point N, then prove that
(i)ar(OMR)=1/2 ar(OQR)
(ii)ar(OMR)=1/4 ar(PQR)
(iii)ar(ONR)=ar(QMN)

Question

Triangle PQR and triangle OMR are two equilateral triangles such
that M is the mid point of PR If OQ intersects PR at point N, then
prove that
(i)ar(OMR)=1/2 ar(OQR)
(ii)ar(OMR)=1/4 ar(PQR)
(iii)ar(ONR)=ar(QMN)

Nishima Pasricha · Accepted Answer

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Triangle PQR and triangle OMR are two equilateral triangles such that M is the mid point of PR. If OQ intersects PR at point N, then prove that (i)ar(OMR)=1/2 ar(OQR) (ii)ar(OMR)=1/4 ar(PQR) (iii)ar(ONR)=ar(QMN)

Triangle PQR and triangle OMR are two equilateral triangles such that M is the mid point of PR. If OQ intersects PR at point N, then prove that
(i)ar(OMR)=1/2 ar(OQR)
(ii)ar(OMR)=1/4 ar(PQR)
(iii)ar(ONR)=ar(QMN)