SOLUTION: A quadrilateral ABCD is inscribed in a points semi-circle with side AD as its diameter. If point O is the center of the semi-circle, determine the angle DCO if angle CAD is 39 degr

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Question 1186475: A quadrilateral ABCD is inscribed in a points semi-circle with side AD as its diameter. If point O is the center of the semi-circle, determine the angle DCO if angle CAD is 39 degrees.
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


(1) AD is the diameter; O is the center
(2) OA, OC, and OD are all radii and so are congruent
(3) Since AD is a diameter, angle ACD is 90 degrees
(4) Angle CAD is 39 degrees, so angle CDA is 51 degrees

Use (2) and (4) to determine the measure of angle DCO

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!


△AOC is isosceles since radii OA and OC are its congruent legs.
Its base angles are congruent so ∠ACO is also 39o.

∠ACD is 90o because it is an angle inscribed in a semi-circle.

So ∠DCO = ∠ACD - ∠ACO = 90o - 39o = 51o.

Edwin