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HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 1 => Topic started by: annaconda on January 31, 2017, 10:30:33 pm

Title: Maths- circle geometry
Post by: annaconda on January 31, 2017, 10:30:33 pm: HI!

For this question, I know the theorem, but I don't know why you have to use the reflex angle and not the 88 degrees.

Thanks :)
Title: Re: Maths- circle geometry
Post by: RuiAce on January 31, 2017, 10:50:50 pm: Quote from: annaconda on January 31, 2017, 10:30:33 pm
HI!

For this question, I know the theorem, but I don't know why you have to use the reflex angle and not the 88 degrees.

Thanks :)
The angle subtended to the centre is twice the angle subtended to the circumference, on the SAME arc. So in this diagram:
(http://i.imgur.com/YQNAKmm.png)
$\begin{align*}\text{obtuse }\angle AOC&=2\angle ABC\\\text{reflex }\angle AOC&=2\angle ADC\end{align*}$
The reflex angle goes to the one on the minor arc, because the major arc is the one SUBTENDING it.
The obtuse or acute angle goes to the one on the major arc, because the minor arc is the one SUBTENDING it.
Title: Re: Maths- circle geometry
Post by: annaconda on January 31, 2017, 10:55:40 pm: Thanks!