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ABCD is an isosceles trapezium with BC = AD = 10 units, AB = 2 units and CD = 14 units. The mid-points of the sides of the trapezium are joined to form a quadrilateral PQRS. Find the ratio of the area of the circle inscribed in the quadrilateral PQRS to the area of trapezium ABCD.
(2015)
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
ABCD is an isosceles trapezium with BC = AD = 10 units, AB = 2 units a...

PQRS is a rhombus, so the centre of the inscribed circle will be the center of the rhombus PQRS

PR = SQ = 8 units
⇒ PQRS is a square

Area of trapezium =   8 = 64 sq. unit.
Required ratio = 
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Most Upvoted Answer
ABCD is an isosceles trapezium with BC = AD = 10 units, AB = 2 units a...

PQRS is a rhombus, so the centre of the inscribed circle will be the center of the rhombus PQRS

PR = SQ = 8 units
⇒ PQRS is a square

Area of trapezium =   8 = 64 sq. unit.
Required ratio = 
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Community Answer
ABCD is an isosceles trapezium with BC = AD = 10 units, AB = 2 units a...

PQRS is a rhombus, so the centre of the inscribed circle will be the center of the rhombus PQRS

PR = SQ = 8 units
⇒ PQRS is a square

Area of trapezium =   8 = 64 sq. unit.
Required ratio = 
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ABCD is an isosceles trapezium with BC = AD = 10 units, AB = 2 units and CD = 14 units. The mid-points of the sides of thetrapezium are joined to form a quadrilateral PQRS. Find the ratio of the area of the circle inscribed in the quadrilateral PQRS to thearea of trapezium ABCD.(2015)a)b)c)d)Correct answer is option 'D'. Can you explain this answer?
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