CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

CAT Questions

The question is from CAT Geometry - Triangles. It discusses about area of an isoceles triangle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. A triangle is inside a circle and some hints are given, we need to find out the area.

Question 18: Circle with center O and radius 25 cms has a chord AB of length of 14 cms in it. Find the area of triangle AOB

1. 144 cm²
2. 121 cm²
3. 156 cm²
4. 168 cm²

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Explanatory Answer

Method of solving this CAT Question from Triangles: The triangle formed by the centre of a circle and the chord is isosceles!! Why?? Think!!!

Given :
Radius of the circle = 25 cm
Center is O
Length of Chord AB = 14 cm
Therefore, △ AOB will be an isosceles triangle with 2 sides OA and OB as 25 cm and side AB as 14 cm.
For an isosceles triangle with the equal sides as 'a' and base as 'b' then

area = \\frac{b}{4}\\) * (4a² - b²)^1/2
Hence Area = \\frac{14}{4}\\) * (4(25)² - 14²)^1/2 = 168cm²

The question is "Find the area of triangle AOB."

Hence, the answer is 168 cm².

Choice D is the correct answer.