Question

In the accompanying diagram of circle O, chords AB and CD intersect at E and
AC:CB:BD:DÀ= 4:2:6:8
What is the measure of AC, BD, and DEB?

Answer 1

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°