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A trapezium DEFG is circumscribed about a circle that has centre at C. If DM = 1 cm, GN = 4 cm and the measure of ∠DEF = ∠EFG = 90°, then find the radius of the circle.
(2012)
  • a)
    2 cm
  • b)
    2.5 cm
  • c)
    2.25 cm
  • d)
    4 cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A trapezium DEFG is circumscribed about a circle that has centre at C....
Let, the radius of circle be 'x' cm.

∴ CM = CN = CR =  x
Given that GN = 4 cm
∴ GP = 4 cm
Also, DP = DM = QN = 1 cm
∴ GD = 5 cm
GQ = GN – QN = 4 – 1 = 3 cm
In ΔDGQ : DQ = 
⇒ 2x = 4 cm (∵ DQ = MN)
∴  x = 2 cm
∴ radius or circle = 2 cm
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Most Upvoted Answer
A trapezium DEFG is circumscribed about a circle that has centre at C....
Let, the radius of circle be 'x' cm.

∴ CM = CN = CR =  x
Given that GN = 4 cm
∴ GP = 4 cm
Also, DP = DM = QN = 1 cm
∴ GD = 5 cm
GQ = GN – QN = 4 – 1 = 3 cm
In ΔDGQ : DQ = 
⇒ 2x = 4 cm (∵ DQ = MN)
∴  x = 2 cm
∴ radius or circle = 2 cm
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A trapezium DEFG is circumscribed about a circle that has centre at C. If DM = 1 cm, GN = 4 cm and the measure of∠DEF = ∠EFG = 90°, then find the radius of the circle.(2012)a)2 cmb)2.5 cmc)2.25 cmd)4 cmCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A trapezium DEFG is circumscribed about a circle that has centre at C. If DM = 1 cm, GN = 4 cm and the measure of∠DEF = ∠EFG = 90°, then find the radius of the circle.(2012)a)2 cmb)2.5 cmc)2.25 cmd)4 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A trapezium DEFG is circumscribed about a circle that has centre at C. If DM = 1 cm, GN = 4 cm and the measure of∠DEF = ∠EFG = 90°, then find the radius of the circle.(2012)a)2 cmb)2.5 cmc)2.25 cmd)4 cmCorrect answer is option 'A'. Can you explain this answer?.
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