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

please see the picture
find the labelled angles
asap
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Last edited by amni1234; February 21st, 2016 at 02:45 PM.
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February 21st, 2016, 03:03 PM   #2
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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
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February 23rd, 2016, 02:00 AM   #3
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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.
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February 23rd, 2016, 05:42 AM   #4
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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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