In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcspictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)a)3/4b)5/6c)1d)7/5e)9/7Correct answer is option 'D'. Can you explain this answer?

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In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs
pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)

a)
3/4
b)
5/6
c)
1
d)
7/5
e)
9/7

Correct answer is option 'D'. Can you explain this answer?

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In the diagram, points A, B, and C are on the diameter of the circle w...

Since the question asks for a ratio, it will be simplest to define the radius of the circle as 1.
Inscribed angle AXY (given as 105¨ intercepts arc ACY. By definition, the measure of an inscribed angle is equal to half the measure of its intercepted arc. Thus arc ACY = 2 x 105 = 210

We are given that points A, B and C are all on the diameter of the circle. Using this information, we can think of arc ACY in two chunks: arc AC plus arc CY. Since arc AC defines a semicircle, it is equal to 180⁰. Therefore arc CY = 210⁰ – 180⁰ = 30⁰

We can now use a proportion to determine the area of sector CBY. Since arc CY represents 30/360 or 1/12 the measure of the entire circle, the area of sector CBY = 1/12 the area of the entire circle. Given that we have defined the circle as having a radius of 1, the area of sector CBY = (1/12) πr2 = (1/12)π(1)2 = π /12.

Next, we must determine the area of the small gray semi-circle with diameter BC. Since BC = 1, the radius of this semi-circle is .5. The area of this semi-circle is 1/2π r2 = (1/2)π (.5)2 = π /8.

Thus, the area of the shaded region below the red line is π /12 + π /8 = 5 π/24.

Now we must determine the area of the shaded region above the red line. Using the same logic as above, angle YBA is 180⁰ – 30⁰ = 150⁰. We can now use a proportion to determine the area of sector YBA.
Since arc YA represents 150/360 or 5/12 the measure of the entire circle, the area of sector YBA = 5/12 the area of the entire circle. Given that we have defined the circle as having a radius of 1, the area of sector YBA = (5/12)r² = (5/12)π(1)² = 5π/12.
We must now determine the area of the small white semi-circle with diameter AB. Since AB = 1, the radius of this semi-circle is .5. The area of this semi-circle is 1/2πr²= (1/2)π(.5)²= π/8
Thus, the area of the shaded region above the red line is

π/12 - π/8 = 7π/24
Finally, then, the ratio of the two areas is (7π/24)/(5π/24) = 7/5. The correct answer is D.

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In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcspictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)a)3/4b)5/6c)1d)7/5e)9/7Correct answer is option 'D'. Can you explain this answer?

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In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcspictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)a)3/4b)5/6c)1d)7/5e)9/7Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcspictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)a)3/4b)5/6c)1d)7/5e)9/7Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcspictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)a)3/4b)5/6c)1d)7/5e)9/7Correct answer is option 'D'. Can you explain this answer?.

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