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AB is a diameter of the circle, CD is a chord equal to the radius of the circle. When AC and BD are extended, they intersect at a point E. Find ∠AEB.
- a)60°
- b)30°
- c)90°
- d)45°
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
AB is a diameter of the circle, CD is a chord equal to the radius of t...
Let the radius of the circle be ‘r’ cm,
Chord CD = r,
In ΔOCD,
⇒ OC = OD = CD = r,
⇒ OCD is an equilateral triangle.
⇒ ∠COD = 60°
⇒ ∠CBD = 30°
⇒ ∠ACB = 90° [angle formed in semicircle]
⇒ ∠ECB = 180° – 90° = 90°
In ΔBCE,
⇒ ∠BEC = 180° – ∠BCE – ∠CBE
⇒ ∠BEC = 60°
∴ ∠AEB = 60°
Most Upvoted Answer
AB is a diameter of the circle, CD is a chord equal to the radius of t...
Since AB is a diameter, it passes through the center of the circle. Let O be the center of the circle. Since CD is a chord equal to the radius of the circle, it is half the length of AB.
Let r be the length of the radius of the circle. Since CD is half the length of AB, CD = r/2.
Since AC and BD are extended, they intersect at a point E. Let AE = x and CE = y.
Applying similar triangles, we have:
x/CE = AE/CD
x/y = (x + r)/(r/2)
2x/y = (2x + 2r)/r
2x/y = (2(x + r))/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
To find the value of x/y, we can cross-multiply:
2x*r = y*(2x + 2r)
2xr = 2xy + 2yr
2xr - 2xy = 2yr
2x(r - y) = 2yr
x(r - y) = yr
x = yr/(r - y)
Now, we know that AC and BD are extended and intersect at E. This means that triangle ABE is similar to triangle CDE. Therefore, we have:
AB/CD = AE/CE
2r/(r/2) = x/y
4r/r = x/y
4 = x/y
Substituting x = yr/(r - y), we have:
4 = yr/(r - y)
4(r - y) = yr
4r - 4y = yr
4r = yr + 4y
4r = y(r + 4)
4r/(r + 4) = y
Therefore, the value of y is 4r/(r + 4).
Let r be the length of the radius of the circle. Since CD is half the length of AB, CD = r/2.
Since AC and BD are extended, they intersect at a point E. Let AE = x and CE = y.
Applying similar triangles, we have:
x/CE = AE/CD
x/y = (x + r)/(r/2)
2x/y = (2x + 2r)/r
2x/y = (2(x + r))/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
2x/y = (2x + 2r)/r
To find the value of x/y, we can cross-multiply:
2x*r = y*(2x + 2r)
2xr = 2xy + 2yr
2xr - 2xy = 2yr
2x(r - y) = 2yr
x(r - y) = yr
x = yr/(r - y)
Now, we know that AC and BD are extended and intersect at E. This means that triangle ABE is similar to triangle CDE. Therefore, we have:
AB/CD = AE/CE
2r/(r/2) = x/y
4r/r = x/y
4 = x/y
Substituting x = yr/(r - y), we have:
4 = yr/(r - y)
4(r - y) = yr
4r - 4y = yr
4r = yr + 4y
4r = y(r + 4)
4r/(r + 4) = y
Therefore, the value of y is 4r/(r + 4).
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AB is a diameter of the circle, CD is a chord equal to the radius of the circle. When AC and BD are extended, they intersect at a point E. Find ∠AEB.a)60°b)30°c)90°d)45°Correct answer is option 'A'. Can you explain this answer?
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AB is a diameter of the circle, CD is a chord equal to the radius of the circle. When AC and BD are extended, they intersect at a point E. Find ∠AEB.a)60°b)30°c)90°d)45°Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about AB is a diameter of the circle, CD is a chord equal to the radius of the circle. When AC and BD are extended, they intersect at a point E. Find ∠AEB.a)60°b)30°c)90°d)45°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB is a diameter of the circle, CD is a chord equal to the radius of the circle. When AC and BD are extended, they intersect at a point E. Find ∠AEB.a)60°b)30°c)90°d)45°Correct answer is option 'A'. Can you explain this answer?.
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