1) Find the value of x of following
a)
110
b)
80
c)
100
c)
60
d)
60
e)
30
f)
120
g)
100
h)
100
i)
70
j)
100
k)
50
l)
48
m)
40
2) If O is the centre of the circle,
3) If O is the centre of the circle,
4) If O is the centre of the circle,
5) If O is the centre of the circle,
6) In the following figure below,
7) In the figure ∆ABC is an equilateral triangle,
8) In the figure measure of arc ABC is 100°
9) figure A,B, C are 3 points on a circle such that the angles subtended by the chord AB and AC at the centre O are 80°, and 120° respectively.
10) In the figure angle BDC=30, ABC=110°,
11) In the given figure O is the centre of the circle. If angle BAC =50°,
12) In the figure below, angle BAP and CPD are 40° and 110,
13) In the figure below, angle ABC and BDC are 110 and 30
14) In the figure below, angle BAC and DBC are 40° and 65°
15)
Calculate the measure of angle AOC. 140
16) In figure, A, B and C are three points on a circle such that angles subtended by the chords AB and AC at center O are 90° and 110°. respectively.
17) In figure, A, B, C are 3 points on a circle such that the angles subtended by chords AB and AC at the centre O are 80° and 120° respectively.
18) figure O is the centre of the circle and the measure of arc ABC is 100°.
19) itn the figure O is the centre of the circle. The angle subtended by the arc BCD at centre 140°. BC is produced to P.
20)
Find angle PQB were O is the centre of the circle. 48
21)
Chord ED is parallel to the diameter AC of the circle. Given angle CBE =65°, find the angle DEC. 25°
22) in the figure O and O' are centres of two circles intersecting at B and C. ACD is a straight line.
23) In the figure O is the centre and PQ is a diameter. If angle ROS=40°
24) In the figure angle ACB=40, angle DPB=120,
25) In the figure AB is the diameter of the circle such that Angle PAB= 40°.
26) In the figure O is the centre of the circle. Angle OAB and OCB are 20 and 55.
EXERCISE-B
1) In the given below,
2) In the following, figure ABCD is a cyclic quadrilateral whose sides AB is the diameter of the circle, through A, B, C, D. If angle ADC =140.
3) ABCD is a cyclic quadrilateral in which AB || CD and Angle B= 65.
4) The opposite angles of a cyclic quadrilateral are in the ratio 4:5. Find the angles in degrees. 80, 100
5) ABCD is a cyclic quadrilateral. If angle BCD and ABD are 100 and 70, then
6) In the figure angle ADC=85
7) In the figure PQRS is a cyclic quadrilateral.
8) In the figure angle DBC and BAC are 70, 40,
9) In the figure angle BDC and ACB are 35 and 40
10) In the given figure t∆ABC is an isosceles triangle with AB =AC and m(angle ABC)=50,
11) ABCD cyclic quadrilateral in which AD|| BC. If angle A= 70,
12) in the given figure below angle ABD=70, angle ADB=30,
13) In the given figure below, angle ACB= 35, angle BDC= 50,
14) in ∆ ABC , BE perpendicular to AC and CF perpendicular to AB which intercept each other at P. if angle A= 40°, find the angle BPC. 140
EXERCISE- C
1) Are the following statements true or false:
a) A quadrilateral whose opposite angles are 85° and 115° is cyclic.
b) A parallelogram whose 1 angle is 100° is cyclic .
c) A rectangle is a cyclic quadrilateral.
d) A square is a cyclic quadrilateral.
e) A rhombus is a cyclic quadrilateral.
f) O is the circumcenter of the ∆ ABC and OD perpendicular to BC. Is angle BOD= angle A.
g) AB is the diameter of a circle and AC and BD are its two parallel chords. Is AD= BC
2) O is the circumcircle of the ∆ ABC . Find the value angleOBC+ angle BAC.
3) who is the circums centre of the triangle ABC find the value of angle OBC A + angle BAC
4) Find the area of a right angled triangle if the radius of a circumcircle is 2 cm. 6
5) Find area right angled triangle if the radius of the circumcircle is 5cn and altitude drawn to the hypotenuse is 4cm. 20
6) ∆ ABC is right angled at B . On AC, a point D is taisecond so that AD = DC and AB = BD. Find angle CAB. 60
7) In the adjoining figure ;
8) In the joining figure angle AOC=110;
9) In the adjoining figure PQ= PR and angle PQR=70
10) In the adjoining figure;
EXERCISE-D
1) In the given figure angle DBC=70 and BAC= 40
2) In the figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If angle BOD=160,
3) In the given figure ∆ ABC is an isosceles triangle with AB= AC and angle=50°.
4) In the figure ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C,D. If angle ADC=130,
5) In the figure C and D are points on the semi-circle described on BA as diameter. Given angles BAD, DBC are 70, 30.
6) In the figure, O is the centre of the circle. The angle subtended by the arc BCD at the centre is 140°. BC is produced to P.
7) In the figure BD = DC and angle DBC = 25.
8) In the given figure angle A=60 and angle ABC =80°,
9) In the figure ∆ABC is an equilateral triangle.
10) In the figure ∆ PQR is an isosceles triangle with the PQ= PR and angle PQR =35.
11) In the figure, O is the centre of the circle. if Angle BOD=160,
12) ABCD is a cycle quadrilateral. If angle BCD =100 and angle ABD=70.
13) In the given figure O is the centre of the circle.
14) In the figure AB and CD are diameters of a circle with centre O. If angle OBD=50
15) On a semi-circle with AB as diameter, a point C is taken, so that angle CAB=30. Find the the angles ACB and ABC . 90,600
16) In a cyclic quadrilateral ABCD if AB|| CD and Angle B =70°, find the remaining angles. 70,110,110
17) In a cyclic quadrilateral ABCD, if angle A= 3 angle C. Find angle A. 135
18) In the figure, O is the centre of the circle and angle DAB=50.
19) In the figure angle BAC=60 and Angle BCA= 20
20) In the figure, if ABC is an equilateral triangle.
21) In the figure O is the centre of the circle. If angle CEA=30,
22) in the figure angle BAD =78 and angle DCF =x° and angle DEF=y°.
23) In a cyclic quadrilateral ABCD, if angle A - angle C=60°. Find the two smaller angles. 60
24) In the figure ABCD is a cyclic quadrilateral.
25) if ABCD is a cyclic quadrilateral in which
a) BC|| AD, angle ADC= 110 and BAC= 50°. Find angle DAC. 60
b) angle DBC=80° and angle BAC=40. Find angle BCD. 60
c) angle BCD= 100 and angel ABD=70. Find angle ADB. 30
26) ABCD is a cyclic trapezium with AD||BC. If angle B=70°, determine other three angles of the trapezium. 110,70, 110
MISCELLANEOUS
1) In the figure O is the centre of the circle.
2) In the figure O is the centre and angle=70.
3) ABCD cyclic quadrilateral EABF is a line such that angEAD=82°, ang FBC= 74, and angBDC=50°. find the obtuse angle between AC and BD. 108
4) Determine the angle a, b and c
105,13,62
5) O is the centre of the circle.
6) In figure, O is the centre of the circle and AP= BP.
7) In the figure, given AB= AC and angle ABC=68.
8) In figure O is the centre of the circle.
9) In the figure, given that PS= SR, ang RPS=54, and ang PRQ= 26,
10) In the figure, O is the centre of the circle.
11) In the figure, given AB|| DC.
12) In the figure ABCD is a cyclic quadrilateral. AE is drawn parallel to CB and DA is produced. If angle ADC =92, angle FAE= 20,
13) In the figure angle A =55° and angle C= 62° and the altitude BE produced meets the circle at D.
14) In the figure if y=x.
15) In the figure angle BCE=30.
16) In the figure I is the in-centre of ∆ ABC . AI when produced meets the circumcircle of triangle of ∆ABC in D. If angle BAC= 66 and angle ACB =80.
17) In the figure, O is the centre of the circle.
a) x b) y c) z d) none
17) In the figure AB=AD= DC=PB and angle DBC =20.
Find the angle ABD, APB. 20,20
18) in the figure O is the centre and AE the diameter of the semicircle ABCDE. If AB= BC and angle AEC=50°, then
19) In the figure, if y= 32 and z= 40,
20) In a triangle ABC, if angle A=60° and the bisectors of Angle B and angle C meets AC and AB at P and Q respectively and intersect each other at I, Find the value of BIC. 120
21) ABCD is a cyclic quadrilateral. If AC bisects both the angles A and C, then find the angle ABC. 90
22) In the figure, O is the centre of the circle and BC = OB.
a) y b) 2y c) 3y d) 4y e) none
23) In the figure, find angle BCD.
24) In the figure O is the centre of the circle arc ABC subtends an angle of 130° at centre O. AB is extended upto P.
