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


  • Correct Answer
    Choice (D). 168 cm2

Detailed Solution

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' the area = * (4 a2 – b2 )
Hence area = * (4(25)2 – 142) = 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.