3. Geomentry
• Geometry is a subject in mathematics that focuses on the study of shapes,
sizes, relative configurations, and spatial properties.
• It is one of the oldest branches of mathematics, having arisen in response
to such practical problems as those found in surveying.
• Geometry will guide you through points, lines, planes, angles, parallel
lines, triangles, similarity, trigonometry, quadrilaterals, transformations,
circles and area.
4. Tips to Solve
1.If a ray stands on a line , than the sum of two adjacent
angle so formed is 180° In the given figure , ray CP
stands on line AB.∠ACD + ∠BCD = 180°.
2. The sum of all angle formed on the same side of a
line at a given point on the line is 180°. In the given figure
four angle are formed on the same side of AOB.
∠AOE + ∠EOD + ∠DOC + ∠COD = 180°.
5. Tips to Solve
3.The sum of all angle around a point is 360° In the given
figure five angle are formed around a point O.
∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA=360°.
4. If two lines A Band CD intersect at a point O, then AOC ,
BOD and BOC , AOD are two pair of vertically opposites
angle Vertically opposite angle are always equal.
∠AOC = ∠BOD and ∠AOD = ∠BOC
6. Tips to Solve
Angle at the Center Theorem:
An angle inscribed across a circle's diameter is always
a right angle:
Cyclic Quadrilateral:
A Cyclic Quadrilateral's opposite angles add to 180°:
a + c = 180°
b + d = 180°
7. Question: Q01
Answer : B
What is measurement of the indicated angle assuming the figure is a square?
A. 45o
B. 90o
C. 60o
D. 30º
8. Question: Q02
Answer : D
If the line m is parallel to the side AB of ?ABC, what is angle a?
A. 125o
B. 25o
C. 65o
D. 50º
9. Question: Q03
Answer : D
Consider the circle shown below having angle AOB as 135º and the shaded portion is
the x part of the circular region. Calculate the value of x.
A. 1/12
B. 1/9
C. 1/6
D. 1/4
10. Question: Q04
Answer : D
AB and CD are two parallel chords on the opposite sides of the center of the circle. If AB = 10 cm,
CD = 24 cm and the radius of the circle is 13 cm, the distance between the chords is
A. 16cm
B. 18cm
C. 15cm
D. 17cm
11. Question: Q05
Answer : C
Find the center of the circle whose equation is x2 + y2 -10x + 12y -10 = 0
A. (5,6)
B. (-5,6)
C. (5,-6)
D. (10,-12)
12. Question: Q06
Answer : A
Find the distance between the points (2,2) and (-1,6)
A. 5 units
B. 4 units
C. 7 units
D. √(26) units
13. Question: Q07
Answer : B
Find the area of the triangle formed by the three points whose coordinates are (2,
3), (4, 5) and (6, 3).
A. 2 units
B. 4 units
C. 3 units
D. 6 units
14. Question: Q08
Answer : A
In a triangle ABC, a circle which touches the edges of all three sides is called
A. In circle
B. Circumcircle
C. Out circle
D. Edge circle
15. Question: Q09
Answer : B
In a triangle a circle passes through the vertices of the triangle, then the circle is called
as
A. In circle
B. Circumcircle
C. Out circle
D. Edge circle
16. Question: Q10
Answer : C
Which of the following is a Pythagorean triplet ?
A. 11 , 40 , 21
B. 3,4,8
C. 25,24,7
D. 26,25,3
17. Question: Q11
Answer : A
A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right
angled at C. If AC is 10 Find the value of CB.
A. 10.5 cm
B. (20/7)√58 cm
C. 12 cm
D. 15 cm
18. Question: Q12
Answer : D
In the given figure, AB is the diameter of the circle with center O. If ∠BOD = 15° &
∠EOA = 85°, then find the value of ∠ECA.
A. 45o
B. 25o
C. 30o
D. 35º
