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Find the number of triangles in the given figure.

Correct Answer: 18

Explanation:

The figure may be labelled as shown.



The simplest triangles are AHB, GHI, BJC, GFE, GIE, IJE, CEJ and CDE i.e. 8 in number.


The triangles composed of two components each are HEG, BEC, HBE, JGE and ICE i.e. 5 in number.


The triangles composed of three components each are FHE, GCE and BED i.e. 3 in number.


There is only one triangle i.e. AGC composed of four components.


There is only one triangle i.e. AFD composed of nine components.


Thus, there are 8 + 5 + 3 + 1 + 1 = 18 triangles in the given figure.


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