CAT Geometry is an important topic that is always covered in MBA exams. It is important because MBA aspirants need to have the diagnostic skill to understand shapes and figures. Some of the topics that are being covered as geometry basics are circles, triangles, parallel lines. Congruency and Similarity of triangles is a chapter that is being intensively concentrated on geometry. A candidate can easily expect 2-3 Geometry question in CAT and also in other MBA exams such as NMAT, XAT, SNAP, etc.
1. A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is
[CAT 2020]
Area of rhombus = 12*16/2 = 96
Let h = radius ; a = diagonal1; b = diagonal2
a = 12
b = 16
AB^2 = (a/2)^2 + (b/2)^2 = 6^2+8^2 = 36+64 = 100
AB = 10
(a/2 * b/2) / 2 = AB * h/2
6*8 = 10*h
H = 4.8
Area of circle = Pi * 4.8 * 4.8
Ratio of areas = Pi * 4.8 * 4.8 /96
On solving = Pi * 6/25
2. In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is
A) 2.5 B) 3.5 C) 0.5 D) 1.5 [CAT 2019]
As per question following figure can be drawn,
As we know AE*BE = CE*DE
X(20.5 –x) = 7*15 = 105
20.5x –x^2 = 105
x^2 -20.5x + 105 = 0
x^2 -10.5x – 10x +105 =0
(x -10)*(x-10.5) =0
So x = 10 or 10.5
Thus if AE = 10 then BE = 10.5 and vice versa
Required difference = (10.5 -10) = 0.5
3. Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is
4. In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
The list of concepts that are covered in basic CAT Geometry are as follows: –
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