My Math Forum Need help in math circle theorems

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February 21st, 2016, 02:30 PM   #1
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Joined: Feb 2016
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Need help in math circle theorems

find the labelled angles
asap
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Last edited by amni1234; February 21st, 2016 at 02:45 PM.

 February 21st, 2016, 03:03 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,781 Thanks: 1432 hints ... 1. sketch in the radius from the center O to the vertex of angle $a$ 2. if O is the center, the 38 degrees is one of two base angles of an isosceles triangle
 February 23rd, 2016, 02:00 AM #3 Newbie   Joined: Feb 2016 From: israel Posts: 17 Thanks: 3 Sorry for my bad french... a triangle inside a circle has some special features. The center of the circle is the point where all the triangle's bisections meet. One more hint: there is a known relation between a central angle and a circumferential angle inside a circle. Last edited by skipjack; February 23rd, 2016 at 02:07 AM.
 February 23rd, 2016, 05:42 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 Two geometric theorems are needed here: The measure of an angle with vertex at the center of a circle is equal to the angle measure of the arc it subtends. The measure of an angle with vertex on the circumference of a circle is equal to half the angle measure of the arc it subtends. Since angles a and b subtend the same arc, we must have measure of angle a equal to half the measure of angle b. Using "A" and "B" to denote those measures, in degrees, B= 2A. Further, with the angle at the center of measure B, the "reflex angle", interior to the quadrilateral, is 360- B. Finally, the interior angles in any quadrilateral add to 360 degrees so we must have 18+ 360- B+ 24+ A= 18+ 360- 2A+ 24+ A= 402- A= 360 so A= 402- 360= 42 degrees and B= 2(42)= 84 degrees.

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