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Vesna [10]
3 years ago
7

In the accompanying diagram of circle O, chords AB and CD intersect at E and

Mathematics
1 answer:
RoseWind [281]3 years ago
6 0

Answer:

m(arc AC) = 72°

m(arc BD) = 108°

m∠DEB = 90°

Step-by-step explanation:

Ratio of the measure of arc AC, arc BC, arc BD and arc AD = 4 : 2 : 6 : 8

Since, m(arc AC) + m(arc CB) + m(arc BD) + m(arc AD) = 360°

By the property of ratio,

Measure of arc AC = \frac{4}{4+2+6+8}\times (360^0)

                               = \frac{4\times 360}{20}

                               = 72°

Measure of arc BD = \frac{6}{4+2+6+8}\times (360^0)

                               = \frac{6\times 360}{20}

                               = 108°

Measure of ∠DEB = \frac{1}{2}m(arcAC + arc BD)

                              = \frac{1}{2}(72+108)

                              = 90°

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