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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

February 12th, 2018, 09:51 AM   #1
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Circle theorems and trigonometry

I am just completely clueless on how to even start on this question, so any help is appreciated.
Attached Images 82A94FD6-09DD-4443-BA90-5DC28BCF28C5.jpg (11.1 KB, 12 views)

Last edited by skipjack; February 12th, 2018 at 01:56 PM. February 12th, 2018, 10:11 AM #2 Newbie   Joined: Dec 2017 From: Spain Posts: 18 Thanks: 1 Could you send another image? I'm not able to read the exercise... February 12th, 2018, 10:41 AM   #3
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From: England

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sorry yes attached below
Attached Images A076ADEE-7707-413B-ADD3-5B073774A7BE.jpg (14.3 KB, 12 views) February 12th, 2018, 12:11 PM #4 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond Can you use the inscribed angle theorem? If so (for part (a)), $$2\angle{BDC}=\angle{BOC} \\ 2\angle{DBC}=\angle{DOC} \\ 2\angle{BDC}+2\angle{DBC}=\angle{BOC}+\angle{DOC}= 180^\circ\implies\angle{BDC}+\angle{DBC}=90^\circ \implies\angle{BCD}=90 ^\circ$$ For part (b), $\overline{OB}=7\sin35^\circ$. Now use the fact that $\triangle{BOC}$ is isosceles $\implies\overline{BC}=2\overline{OB}\cos70^\circ$ . Last edited by greg1313; February 14th, 2018 at 02:10 AM. February 12th, 2018, 01:54 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,386 Thanks: 2012 As $OB = OC = OD$, $\angle OCB = \angle OBC = 70^\circ$ and $\angle ODC = \angle OCD$. Hence $\angle DOC = 140^\circ$, and so $\angle ODC + \angle OCD = 40^\circ$. It follows that$\angle OCD = 20^\circ$, and so $\angle BCD = 70^\circ + 20^\circ = 90^\circ$. You could alternatively obtain $\angle BCD$ in one step by use of the alternate segment theorem, which states that the angle between the tangent and chord equals the angle in the alternate segment. As $\sin(35^\circ) = OB/(7\text{ cm})$ and $\cos(70^\circ) = (BC/2)/OB$, $BC = 2\sin(35^\circ)\cos(70^\circ)\times 7\text{ cm}$, which can be evaluated by use of a calculator. If you're required to specify every theorem that you've used, you would need to add a few details to the above. Tags circle, theorems, trigonometry Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jamesbrown Trigonometry 5 September 15th, 2016 12:12 PM Tangeton Geometry 1 March 10th, 2016 07:40 PM amni1234 Geometry 3 February 23rd, 2016 04:42 AM peterle1 Algebra 2 February 11th, 2010 10:46 AM David_Lete Algebra 5 April 11th, 2009 04:20 AM

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