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kenny6666 [7]
3 years ago
12

Point D is the center of the given circle.What is the measure of arc AC?

Mathematics
2 answers:
malfutka [58]3 years ago
8 0
∠ABC is an inscribed angle.
In a circle, the measure of an inscribed angle is half the measure of the intercepted arc.  m∠ABC = 48°  ⇒
measure of arc AC = 2*m∠ABC = 2 * 48 = 96°.
Dahasolnce [82]3 years ago
5 0
ANSWER

D. \: \: 96\degree

EXPLANATION

The measure of angle ABC is 48°.

Angle about the center is twice the angle about the edge.

The measure of angle ADC is twice the measure of angle ABC.

This implies that,

m \: < \: ADC=2(m \: < \: ABC)

We substitute to obtain,

m \: < \: ADC=2(48 \degree)

We simplify to get,

m \: < \: ADC=96 \degree

Hence the measure of arc AC is 96°.

Therefore the correct answer is option D.
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