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# Math: Circles

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Intern
Joined: 20 Feb 2016
Posts: 4

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19 Jun 2016, 09:10
Very helpful. It helped clear a lot of my concepts on circles.
Manager
Joined: 01 Sep 2016
Posts: 98

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13 Sep 2016, 13:11
Quite a Refresher

Bunuel wrote:
chauhan2011 wrote:
• If you know the length of the minor arc and radius, the inscribed angle is: 90L/nr

Please correct me if i am wrong but i think the formula should be : 180L/nr

If you know the length $$L$$ of the minor arc and radius, the inscribed angle is: $$Inscribed \ Angle=\frac{90L}{\pi{r}}$$.

The way to derive the above formula:

Length of minor arc is $$L= \frac{Central \ Angle}{360}* Circumference$$ --> $$L= \frac{Central \ Angle}{360}* 2\pi{r}$$ --> $$L= \frac{Central \ Angle}{180}* 2\pi{r}$$ --> $$Central \ Angle=\frac{180L}{\pi{r}}$$ (so maybe you've mistaken central angle for inscribed angle?).

The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle: $$Central \ Angle=2*Inscribed \ Angle$$.

So, $$2*Inscribed \ Angle=\frac{180L}{\pi{r}}$$ --> $$Inscribed \ Angle=\frac{90L}{\pi{r}}$$.

Hope it helps.
Senior Manager
Joined: 09 Feb 2015
Posts: 381
Location: India
Concentration: Social Entrepreneurship, General Management
GMAT 1: 690 Q49 V34
GMAT 2: 720 Q49 V39
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17 Aug 2017, 13:36
Bunuel
I have a doubt here . Consider the last figure! If the lines OA and OB are drawn, what will be the resulting Angle OAP and OBP ?
Re: Math: Circles   [#permalink] 17 Aug 2017, 13:36

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