From the first figure to the second figure the middle design rotates through 90° and moves to the extreme right position after being reduced in size and the lower most design encloses the inverted and reduced upper most design.
The simplest triangles are GLK, DLJ, DJM, HMN, QRE, IRA, IPA and FPO i.e. 8 in number.
The triangles having two components each are BDO, CDQ, DLM, PRA, KFI, NEI, HJI, GJI, DKI and DNI i.e. 10 in number.
The triangles having four components each are DIE, DFI, DOA, DQA andGHI i.e. 5 in number.
The triangles having six components each are DCA and DBA i.e. 2 in number.
DEF is the only triangle having eight components.
ABC is the only triangle having twelve components.
Thus, there are 8+10+ 5 + 2+1 + 1 = 27 triangles in the figure.
From first figure to second figure to the left of sign (::), the triangle is converted into square, i.e., one side is added to each design and a circle is introduced inside the concentric squares touching the sides.
The simplest triangles are AEH, EHI, EBF, EFI, FGC, IFG, DGH and HIG i.e. 8 in number.
The triangles composed of two components each are HEF, EFG, HFG and EFG i.e. 4 in number.
Thus, there are 8 + 4 = 12 triangles in the figure.
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