Consider triangle ABC.If 206 lines are drawn from A to BC how many triangles are formed?


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Question Number 36398 by NECx last updated on 01/Jun/18

$C o n s i d e r t r i a n g l e A B C . I f 206$ $l i n e s a r e d r a w n f r o m A t o B C h o w$ $m a n y t r i a n g l e s a r e f o r m e d ?$
Commented by Rasheed.Sindhi last updated on 02/Jun/18

$207 + 206 + . . . + 1 = \frac{207 \times 208}{2} = 21528$ $(including △ ABC)$
	Answered by tanmay.chaudhury50@gmail.com last updated on 01/Jun/18

	$t o t a l l i n e s 206 + A B + A C + B C$ $t o t a l p o i n t s o n B C f o r t h e s e 206 l i n e s = 206$ $t o t a l p o i n t s i n B C = 2 o 6 + p o i n t B a n d C$ $a n y t w o p o i n t s o u t o f t h e s e 206 + 2 = 2 o 8 p o i n t s$ $w h e n j o i n w i t h p o i n t A . . . m a k e$ $t r i a n g l e$ $s o n u m b e r o f t r i a n g l e s = 2 o 8 C_{2} - 1$ $h e r e e 1 s u b s t r u c t e d f o r t r i a n g l e A B C$
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