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April 9th, 2018, 08:33 AM   #1
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How ratios are written here?

In the below figure, O is the center of the circle. Radius is 7 cm. $\angle$ BOC = 120 Find the length of BC?



Solution: Join AO to meet BC in M

$\triangle ABC \cong \triangle AOC$

$\triangle BMO \cong \triangle CMO$

$\angle BMO$ = 90

Triangle BMO has three angles are 90, 60 and 30.

The sides are in the ratio of 2: $\sqrt 3$ : 1

2X = 7 $\Rightarrow$ X = 7/2

BM = $\Rightarrow$ $\sqrt 3$ x 7 / 2 = 7$\sqrt 3 / 2$

BC = 2 x 7$\sqrt 3 / 2$ = 7 $\sqrt 3$

My Question is: How ratios are written here?

Last edited by Ganesh Ujwal; April 9th, 2018 at 08:36 AM.
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April 9th, 2018, 12:20 PM   #2
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Latex input \$\dfrac{a}{b}\$ will yield $\dfrac{a}{b}$
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April 9th, 2018, 02:29 PM   #3
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Triangle BMO is half of an equilateral triangle, so MO = 3.5cm.
Now apply Pythagoras to find BM.
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April 9th, 2018, 06:36 PM   #4
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Quote:
Originally Posted by skeeter View Post
Latex input \$\dfrac{a}{b}\$ will yield $\dfrac{a}{b}$
Are you trolling ? I know how ratios are written in tex command.
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April 9th, 2018, 06:43 PM   #5
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Quote:
Originally Posted by skipjack View Post
Attachment 9579
Now apply Pythagoras to find BM.
Why you think $\angle$ BMO is right angled triangle?

Don't tell me I told $\angle$ BMO is 90. Use your own method and prove me.
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April 9th, 2018, 11:27 PM   #6
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Quote:
Originally Posted by Ganesh Ujwal View Post
Are you trolling ? I know how ratios are written in tex command.
Then what are you asking??

-Dan
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April 10th, 2018, 01:33 AM   #7
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How is the ratio obtained at the step shown in the solution?
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April 10th, 2018, 03:04 AM   #8
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The diagram is symmetrical about AO, so angles BMO and CMO have equal measure, which implies they are right angles; also angles BOM and COM have equal measure, which implies they are both 60$^\circ$.

Knowing the angles of triangle BMO are 90$^\circ$, 60$^\circ$ and 30$^\circ$ implies that it is half of an equilateral triangle.
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April 10th, 2018, 07:33 AM   #9
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Quote:
Originally Posted by skipjack View Post
The diagram ....... triangle.
My question is different. How ratios are obtained?

I got the answer myself: http://mathcentral.uregina.ca/qq/dat....05/gary1.html

Can you tell me how 2X = 7 is obtained in my solution?

Last edited by Ganesh Ujwal; April 10th, 2018 at 07:46 AM.
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April 10th, 2018, 09:17 AM   #10
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I got the answer myself: 2x = 7 because 2 x is hypotenuse. Here hypotenuse is radius of the circle i.e 7.
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