P and Q are the mid-points of 
and 
in ΔABC. If the area of ΔAPQ = 12√3, find the area of ΔABC.
In ∆ABC, P and Q are mid-points of AB and AC respectively.
The correspondence ∆APQ↔∆ABC is a similarity by SSS theorem.
Now,
Areas of similar triangles are proportional to the squares of their corresponding sides.
ABC = 12√3 × 4
ABC = 48√3
The area of ∆ABC is 48√3.
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and 
intersects 
in M and 
in O. Prove that AM2 = MT • MO.
. 
and 
intersect in N. Prove that DN = 2MN.
= {0}. Prove that the area of ΔOAB = 
(area of
= {T}, PS = QR,
. Prove that ΔTPS is similar to ΔQTR.