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Form 2 Angle Properties of a Circle Questions and Answers
Copy and complete the table below. All angles are subtended by the same arc.
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1.
Find the values of x and y from the given
2.
Find the values of x and y
3.
In the figure below, calculate #angle#LNP if #angle#PLM = 70° and #angle#KNL = 42°.
4.
In the figure below, 0 is the centre of the circle. The reflex angle AOD = 256° and #angle#ACE = 50°. Calculate: (a) #angle#BDC (b) #angle#BAE.
5.
In the figure below, #angle#VUZ = 110° and #angle#XVY = 30°. Find the value of #angle#VWY.
6.
In the figure below, 0 is the centre of the circle and BA is parallel to CD. If #angle#BAC = 31°, calculate #angle#BCO and #angle#ADE.
7.
In the figure below, WXYZ is a cyclic quadrilateral and VWZ a straight line. Angle VWX = 97° and #angle#XZY = 43°. Calculate the size of angle ZXY.
8.
Copy and complete the table below. All angles are subtended by the same arc.
9.
In the figure below, O is the centre or the circle. Find obtuse #angle# AOB.
10.
The figure below shows a circle with the centre at 0: Find the values of a, b, c and d if #angle# PQO = 40° and #angle# PSO = 30°.
11.
In the figure below, O is the centre of the circle. Show that the reflex angle #angle# POR = 2 #angle# PQR.
12.
In figure below, O is the centre of the circle. LN and PM are diameters. Show that LM is parallel to PN:
13.
In the figure below, O is the centre of the circle. Calculate x.
14.
In the figure below, O is the centre of the circle and POM is the diameter. If #angle#QLK = 73°, calculate #angle#QNM:
15.
In the figure below, O is the centre of the circle and DOB is the diameter. Find x and y if ABCO is a rhombus and #angle#AOD =120°.
16.
In the figure below, O is the centre of the circle. BOD is the diameter, AC=BC and #angle#BAC = 25°. Find the size of: (a) #angle#AOD. (b) #angle#BAO.
17.
AB and CD are intersecting chords of a circle with centre O. If AB is the diameter of the circle, show that: (a) #angle#AOC = 2 #angle#ABC. (b) ADB = 90°.
18.
Two circles with centres O and R intersect at P and Q as shown in the figure below. OR cuts the circles at S and T respectively. If #angle#AOR = 150° and #angle#BRO = 120°, find a, b and c.
19.
In a circle KLMN with centre O, the diagonals of quadrilateral KLMN intersect at R #angle#LKM=38°, #angle#LNK = 64° and #angle#KRN = 82°. Find: (a) #angle#KNM. (b) #angle#LMN. (c) #angle#KLM.
20.
The figure below shows a circle ABCD, centre O. BO is perpendicular to the diameter AOD and #angle#COD = 30°. Calculate. (a) #angle#BCA. (b) #angle#CAD.
21.
ACB is a circle, centre O, with diameter AB perpendicular to BD as shown in the figure below. If BC = BD = CD and DO is perpendicular to BC, find p and t.
22.
Find the values of a and b in the figure below.
23.
In the figure below, calculate the angles marked v, w, x, y and z:
24.
In the figure below, O is the centre of circle ABCDE and BOE is the diameter: #angle#COD = 80° and CB = CD. Calculate the angles marked p, q, r and s.
25.
In the figure below, 0 is the centre of the circle. Find the values of x and y.
26.
Find the angles marked by small letters.
27.
In the figure below, O is the centre of the circle. Calculate the value of angle a.
28.
Find the value of x and y.
29.
Two equal chords WX and YZ are produced to meet at T. If #angle#WYX = 73° and #angle#YZW = 37°, show that #angle#TZX = #angle#XWY = 70°.
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