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 April 8th, 2018, 11:12 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 183 Thanks: 1 How angle ACB is 90? In circle ABC where O is the center, there is a triangle ABC. but how angle ACB is 90?
 April 8th, 2018, 11:52 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,780 Thanks: 1025 Math Focus: Elementary mathematics and beyond That result is known as Thales's theorem. Thanks from topsquark
 April 9th, 2018, 03:49 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,089 Thanks: 846 A more general theorem is that if an angle is inscribed in a circle (all three vertices on the circle) then the angle measure is half the measure of the arc it cuts off. Since AB goes through the center, O, it is a diameter. What is the measure of the arc AB? So what is the angle ACB?
 April 9th, 2018, 03:50 AM #4 Newbie   Joined: Sep 2017 From: Saudi Arabia Posts: 27 Thanks: 2 The angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at the circumference of that circle. The angle AOB is twice the angle ACB. ******************** In our case, the angle AOB = 180 degrees, so the angle ACB must be half of the angle AOB = (1/2)*(180) = 90 degrees.
 April 9th, 2018, 06:51 AM #5 Global Moderator   Joined: Dec 2006 Posts: 18,838 Thanks: 1564 As triangles AOC and BOC are isosceles, $\small\angle$ACB = $\small\angle$ACO + $\small\angle$BCO = $\small\angle$CAO + $\small\angle$CBO. Hence $\small\angle$ACB is half the sum of the internal angles of triangle ABC.
April 9th, 2018, 07:54 AM   #6
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Quote:
 Originally Posted by Hussain2629 ......
Please try to minimize the image size from next time.

April 9th, 2018, 10:10 PM   #7
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Quote:
 Originally Posted by Ganesh Ujwal Please try to minimize the image size from next time.
Sorry for that dear.. I will minimize next time.... I hope my answer was clear for you.

 April 16th, 2018, 06:48 AM #8 Newbie   Joined: Mar 2018 From: Washington Posts: 6 Thanks: 0 Math Focus: Geometry Is it obvious to me alone? Using Thales's theorem is all easy. Usually if I do not understand something, I'll first read all the relevant information, if I have not found my answer, then I ask other sources starting from mathforums ending with help sites in homework. Thanks to this, I now feel much more strongly in various fields of activity. Learn while young. Last edited by skipjack; April 16th, 2018 at 07:12 AM.
 April 16th, 2018, 08:01 AM #9 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,074 Thanks: 794 Scotty, can we buy you a one-way ticket to another site?
 April 16th, 2018, 09:45 AM #10 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,089 Thanks: 846 Behave, Denis! Thanks from Denis

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