Importance:
It is considered as the most important topic for SSC Exams.
You can find at least 10 questions in SSC CGL/ CHSL Tier-2 and 3-4 questions in Tier-1 from Geometry itself.
Some Important Properties and Formulae:
Model Questions
1. The sides of a triangle are 13 cm, 84 cm, 85 cm, what is the radius of the circle circumscribing the triangle?
A) 40.5 cm B) 42.5 cm
C) 30.5 cm D) 44 cm
2. The sides AB and AC of DABC are produced to P and Q respectively. The bisectors of ÐCBP and ÐBCQ meet at R. If the measure of ÐA = 64° then what is the measure of 
DBRC?
A) 60° B) 64° C) 32° D) 58°
3. In DABC, AB = 10 cm, AC = 13 cm and BC = 46 cm. If AD is the angle bisector of DBAC, where D is a point on BC, then BD is equal to:
A) 20 cm B) 10 cm C) 16 cm D) 23 cm
4. If each interior angle of a regular polygon is 144°, then what is the sum of the number of its diagonals and no. of its sides?
A) 16 B) 50 C) 30 D) 45
5. PQRS is a cyclic quadrilateral in which PQ = 20 cm, QR = 18 cm and SR = 12 cm. If PR bisects QS, what is the length of PS?
A) 40 cm B) 60 cm C) 30 cm D) 45 cm
6. In Quadrilateral ABCD, the bisectors of ÐA and ÐB meet at O and ÐAOB = 73°, 
DC + 
DD is equal to....
A) 146° B) 145° C) 90° D) 36°
7. A circle is inscribed in DABC, touching AB, BC and AC at the points P, Q, R respectively. If AB − BC = 5 cm, AB − AC = 3 cm and the perimeter of DABC = 20 cm, then PB + AR is equal to:
8. In DABC, D and E are the points on the sides AB and BC respectively, such that DE || AC. If AD : DB = 6 : 5, then what is the ratio of the area of DBDE to that of trapezium ADEC?
A) 25 : 96 B) 25 : 121 C) 40 : 53 D) 5 : 6
9. If DABC, ÐA = 74°. If I is the incentre of the triangle, then the measure of 
DBIC is....
A) 145° B) 74° C) 148° D) 127°
10. In a trapezium ABCD, AB || CD, AB = 14 cm and CD = 8 cm. What is the length of the line segment joining the midpoints of its diagonals?
A) 9 cm B) 11 cm C) 3 cm D) 6 cm
Key
1-B 2-D 3-A 4-D 5-C 6-A 7-B 8-A 9-D 10-C
Explanations
1. 13 cm, 84 cm, 85 cm is a Pythagoras triplet.
So, Circum radius in a right angled triangle
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