## Question

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4 (√2 – l) cm, then the area, in sq cm, of the triangle ABC is

16

## Solution

From CAT 2017 – Quantitative Aptitude – Geometry – Triangles, we can see that,

PQ = PR = PS = 4(√2-1)
CS = PR
(PC)^2 = (PS)^2 + (CS)^2
On solving, we get, PC = 4√2(√2-1)
So, QC = PC + PQ = 4
Area of a right angled triangle = ½ * Base * Height
So, ½ * AC * BC = ½ * QC * AB
On solving, we get a = 4√2
Area of triangle = ½ * a^2 = 16

## CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Triangles – Q1: 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 – Q2: 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.
Quantitative Aptitude – Geometry – Circles – Q1: 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 – Circles – Q2: 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 – 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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## Question

Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is

24

## Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Triangles,
BC^2 = AB^2 + AC^2 = 625
BC = 25
Shortest Distance from A to hypotenuse = altitude on BC = AP
AP * BC = AB * AC
So, AP = 12
Time taken = (12/30) * 60 mins = 24 mins

## CAT 2017 Questions from Quantitative Aptitude – Geometry

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: 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.
Quantitative Aptitude – Geometry – Circles – Q1: 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 – Circles – Q2: 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 – 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

## 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

## Question

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

A) 225√3
B) 500 / √3
C) 275 / √3
D) 250 / √3

Option (B)

## Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Triangles,
Area of triangle = root (s(s-a)(s-b)(s-c))
S = 50
Area = 250 * root(3)
Centroid divides triangle in the ratio 2:1
Area of remaining portion of triangle: 2/3 * (Area of Triangle) = 500/root(3)
Option (B)

## CAT 2017 Questions from Quantitative Aptitude – Geometry

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 – Circles – Q1: 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 – Circles – Q2: 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 – 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

## 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