Geometry At It's Best

Geometry Level 5

In the Fig. \(\triangle ABC\) is such that \(D \ \& \ E \) lie on \(AB\) and \(F \ \& \ G \) lie on \(BC\).

  • \(D\) and \(E\) are points of trisection of \(AB\).

  • \(F\) divides \(BC\) in the ratio \( 1:3\) and \(G\) divides \(BC\) in the ratio \(3:1\)

\(AF , AG , CD \ \& \ CE \) are drawn such that they intersect to form \(\Box PQSR\)

\( \dfrac{A(\triangle ABC)}{A(\Box PQSR)}=\dfrac{m}{n}\)

Find \(m-n\)


Details and Assumptions:-

  • \(gcd(m,n)=1\)
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