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Answer :
Final answer:
In this figure, we have a circle with two radii, OA and OB, and two chords, AD and BD. The central angle BOA measures 250 degrees. We need to find m∠BDA and m∠BCA. To find m∠BDA, we can use the fact that the measure of an angle formed by a chord and a tangent at the same endpoint is half the measure of the intercepted arc. To find m∠BCA, we can use the fact that the measure of an angle formed by two intersecting secants is half the difference of the intercepted arcs.
Explanation:
In this figure, we have a circle with two radii, OA and OB, and two chords, AD and BD. Secants BC and AC are drawn that intersect each other outside the circle at point C. The central angle BOA measures 250 degrees. We need to find:
m∠BDA and m∠BCA.
To find m∠BDA, we can use the fact that the measure of an angle formed by a chord and a tangent at the same endpoint is half the measure of the intercepted arc. Since m∠BOA is 250 degrees, the intercepted arc AB is also 250 degrees. Therefore, m∠BDA = 250/2 = 125 degrees.
To find m∠BCA, we can use the fact that the measure of an angle formed by two intersecting secants is half the difference of the intercepted arcs. Since the intercepted arcs are BA and BC, and m∠BOA is 250 degrees, the intercepted arcs are 250 degrees and the difference is 250 - 125 = 125 degrees. Therefore, m∠BCA = 125/2 = 62.5 degrees.
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