Quantitative Aptitude - Geometry - Circles - ABCD is a quadrilateral inscribed
Quantitative Aptitude - Geometry - Circles
Question
ABCD is a quadrilateral inscribed in a circle with centre O. If âˆ COD = 120 degrees and âˆ BAC = 30 degrees, then the value of âˆ BCD (in degrees) is
Answer
90
Solution
From CAT 2017 - Quantitative Aptitude - Geometry - Circles, we can see that,
OD = OC (Radius of circle)
So, angle (ODC) = angle (OCD) = 30 deg
Angle (DOA) = 60 degrees
Angle (BAC) = 30 degrees (Given)
OA = OD (radius of circle)

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Quantitative Aptitude - Geometry - Circles - Let ABC be a right-angled isosceles
Quantitative Aptitude - Geometry - Triangles
Question
Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is
A) 9Ï€ - 18
B) 18
C) 9Ï€
D) 9
Answer
Option (B)
Solution
As per the question from CAT 2017 - Quantitative Ap

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Quantitative Aptitude â€“ Geometry - Circles â€“ A chord of length 5 cm subtends an
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Circles â€“ A chord of length 5 cm subtends an
A chord of length 5 cm subtends an angle of 60Â° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120Â° at the centre of the same circle is?
a) 6âˆš2
b) 8
c) 4âˆš2
d) 5âˆš3
Answer: d) 5âˆš3
Solution:
In triangle ODA, OA=AD cosec 30=5
So if the angle AOB is 120 degree, then angle AOD will be 120/2=60

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Quantitative Aptitude â€“ Geometry - Circles â€“ In a circle with center O and radius 1 cm
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Circles â€“ In a circle with center O and radius 1 cm
In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is?
a) (Ï€/6)^(1/2)
b) (Ï€/(4âˆš3))^(1/2)
c)

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Quantitative Aptitude â€“ Geometry - Circles â€“ In a circle, two parallel chords on the same side
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Circles â€“ In a circle, two parallel chords on the same side
In a circle, two parallel chords on the same side of diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is?
a) âˆš11
b) âˆš13
c) âˆš12
d) âˆš14
Solution:
Option b) âˆš13 is correct
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