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In the figure AB and CD are two diameters
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16 Jun 2021, 02:45
16 Jun 2021, 02:45
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84% (03:04) correct
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In the figure, AB and CD are two diameters of circle such that ∠COA = 48°. If E is any point on arc CB, what is the measure of ∠CEB
A. 114°
B. 100°
C. 80°
D. 96°
E. 40°
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In the figure AB and CD are two diameters
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16 Jun 2021, 05:08
16 Jun 2021, 05:08
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Carcass wrote:
In the figure, AB and CD are two diameters of circle such that ∠COA = 48°. If E is any point on arc CB, what is the measure of ∠CEB
A. 114°
B. 100°
C. 80°
D. 96°
E. 40°
Important: Since AB and CD are both diameters, their point of intersection (point O) must be the center of the circle.
Let's use some useful circle properties
First let's add a blue line, to divide ∠CEB into 2 angles
CD is the DIAMETER of the circle
Since ∠CED is an inscribed angle containing (aka "holding") the diameter, we can conclude that ∠CED = 90°
Now recognize that the intersection of AB and CD creates two equal (vertically opposite) angles, we can conclude the angle opposite the 48° is also 48°
Now recognize that we have two angles containing (aka "holding") the arc BD
Property: If a CENTRAL angle and an INSCRIBED angle contain the same arc, then the CENTRAL angle is TWICE the INSCRIBED angle
This means that ∠DEB = 24°
At this point, we have:
So, ∠CEB = 90° + 24° = 114°
Answer: A
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Re: In the figure AB and CD are two diameters
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02 Jan 2022, 10:41
02 Jan 2022, 10:41
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