# CAT Practice : Coordinate Geometry

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The triangle formed by the centre of a circle and the chord is isosceles!! Why?? Think!!!

## Area of an isosceles triangle

Q.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

Choice (D). 168 cm2

## Detailed Solution

Given :
Radius of the circle = 25 cm
Center is O
Length of Chord AB = 14 cm

Therefore, $\triangle$ 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' the area = $\frac{b}{4}$ * (4 a2 – b2 )${\frac{1}{2}}$
Hence area = $\frac {14}{4}$ * (4(25)2 – 142)${\frac{1}{2}}$ = 168 cm2

Correct Answer: 168 cm2

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.