## Question

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

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)

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

## 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

: 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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