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Question Number 184041 by Acem last updated on 02/Jan/23

	Answered by HeferH last updated on 02/Jan/23

	$\overset{⌢}{T N} = \frac{π}{3} = \frac{180 °}{3} = 60 ° \Rightarrow ∠ T A N = \frac{\overset{⌢}{T N}}{2} = 30 °$ $∠ A O T = 120 ° (△ A O T i s o s c e l e s)$ $∠ A T C = \frac{\overset{⌢}{A T}}{2} = 60 \Rightarrow ∠ A C T = 90 °$ $M T C A i s c y c l i c,$ $t h e c e n t e r w o u l d b e t h e m i d p o i n t o f A T$
	Answered by mr W last updated on 02/Jan/23

	Commented by mr W last updated on 02/Jan/23

	$∠ T A N = \frac{\overset{⌢}{T N}}{2} = 30 °$ $∠ B O T = 2 ∠ O A T = 60 ° = ∠ O A C$ $\Rightarrow A C / / O T$ $\Rightarrow A C ⊥ B C$ $\Rightarrow ∠ A C B = 90 ° = ∠ A M T$ $\Rightarrow A C T M a r e c y c l i c, l i e o n a c i r c l e$ $w i t h A T a s d i a m e t e r . M i d p o i n t$ $o f A T i s t h e c e n t e r .$
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