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The vertices of a triangle are (0,0) - Quantitative Aptitude - Geometry

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The question below is from previous year CAT question from CAT 2020 exam comes from CAT Geometry: The vertices of a triangle are (0,0)

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills.

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CAT 2020 - Slot 3 - Quantitative Aptitude - Geometry - Question 19 - The vertices of a triangle are (0,0)

Q. 19: The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is 

1.  
2. 
3. 
4. 

C.

A circle is circumscribed on the points (0,0) (4,0) and (3,9)

We are asked to find the area of this circle

 

We know that the area of a triangle with sides a, b and c, inscribed ina circle of radius R is given by

Area = 

 With the help of teh co-ordinates of the triangle it is easy to find the height of the triangle, which is QS = 9 units.
Hence the area of the triangle = A = 1/2 × base × height = 1/2 × PR × QS = 1/2 × 4 × 9 = 18 sq. units
a = PR = 4 units
b = QR = √(QS2 + SR2) = √(92 + 12) = √82
c = PQ = √(PS2 + PQ2) = √(32 + 92) = √90
Now that we know the radius of the circle the area of the circle = π × R2 = π × 

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