Quantitative Aptitude – Geometry – Circles – ABCD is a quadrilateral inscribed

Quantitative Aptitude – Geometry – Circles

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Geometry - Circles - ABCD is a quadrilateral inscribed
ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is

Answer

90

Solution

From CAT 2017 – Quantitative Aptitude – Geometry – Circles, we can see that,
Quantitative Aptitude - Geometry - Circles - ABCD is a quadrilateral inscribed
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)
Angle (ODA) = angle (OAD) = 60 deg
Sum of Opposite angles in a cyclic quad are 180 deg
Angle (BAD) + angle (BCD) = 180
So, angle (BCD) = 90 deg
Answer: 90 degrees

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Circles – Ques: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.
Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.
Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.
Quantitative Aptitude – Geometry – Triangles – Q3: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Quantitative Aptitude – Geometry – Coordinate – Q2: The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is
Quantitative Aptitude – Geometry – Mensuration
Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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Mensuration Basics and 3-Dimensional Geometry Concepts for CAT

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Quantitative Aptitude – Geometry – Circles – ABCD is a quadrilateral inscribed
5 (100%) 51 votes

Quantitative Aptitude – Geometry – Circles – Let ABC be a right-angled isosceles

Quantitative Aptitude – Geometry – Triangles

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Geometry - Circles - Let ABC be a right-angled isosceles
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) 9π – 18
B) 18
C) 9π
D) 9

Answer

Option (B)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Circles,
Quantitative Aptitude - Geometry - Circles - Let ABC be a right-angled isosceles
Let AB = a (a = 6)
CQB is a semicircle of radius a/√2
CPB is a quarter circle (quadrant) of radius a
So, area of semicircle = pi*a^2/4
Area of quadrant = pi*a^2/4
So, area of region enclosed by BPC, BQC = Area of tr(ABC) = 18.
Option (B)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Circles – Ques: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.
Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.
Quantitative Aptitude – Geometry – Triangles – Q3: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Quantitative Aptitude – Geometry – Coordinate – Q2: The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is
Quantitative Aptitude – Geometry – Mensuration
Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

Other posts related to Quantitative Aptitude – Geometry

Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 1
Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 2
Geometry Basics for CAT – Triangle related questions and problems
Mensuration Basics and 3-Dimensional Geometry Concepts for CAT
​​

Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

Know More about Online CAT Course

Quantitative Aptitude – Geometry – Circles – Let ABC be a right-angled isosceles
5 (99.64%) 55 votes