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anonymous

  • one year ago

How do you prove properties of angles for a quadrilateral inscribed in a circle?

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  1. phi
    • one year ago
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    each of the angles in the quadrilateral is an "inscribed angle" in the circle and we know inscribed angles are equal to 1/2 of the "intercepted arc" notice the inscribed arcs of two angles that are opposite each other form an entire circle see figure |dw:1438958135190:dw|

  2. phi
    • one year ago
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    and now with its opposite angle|dw:1438958219451:dw|

  3. phi
    • one year ago
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    and we know the two arcs must add up to 360 degrees (i.e. all the way round a circle) and because the angles are 1/2 of their arcs, the angles sum up to 180 degrees (1/2 of 360)

  4. anonymous
    • one year ago
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    @phi Thanks! :)

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