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Form 3 Mathematics Angle Properties of a Circle Questions and Answers
In the figure below, O is the centre of the circle and #angle# OAC=#38^0#. Find #angle# ABC.
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1.
In the figure below, O is the centre of the circle. Angle OAB =#30^0# and angle BAC =#23^0#. Find the angle ACB.
2.
In the figure below, O is the centre of the circle. PQ and PR are tangents. Angle PQS=#40^0 #and angle PRS=#30^0# Find angle (i) RTQ (ii) ORQ (iii) RPQ
3.
In the figure below (not drawn accurately) PAQ is a tangent to the circle at A. Find the #angle#DAB and #angle#BAQ.
4.
In the figure alongside O is the centre of the circle. Angle BAC =#50^0# and angle ABO=#20^0#. Determine the size of angle ACB.
5.
In the figure below, ABC is the tangent to the circle at B. #angle#ABG=#42^0# and #angle#FEG=#20^0#. (a) Find (i) #angle#BGF (ii) #angle#BDF (b) If BE bisects #angle#GED, find #angle#DBC
6.
In the figure below, O is the centre of the circle and #angle# OAC=#38^0#. Find #angle# ABC.
7.
The figure below (not drawn to scale) shows a circle PQRS centre O with SR produced to T. PQ//SR and #angle# QSR=#35^0#. Calculate the size of #angle# QRT
8.
In the figure below, #angle# CAD=#20^0#, #angle# AFE=#120^0# and BCDF is a cyclic quadrilateral. Find #angle# FED.
9.
In the figure besides, CP=CQ and #angle# CQR=#160^0#. If ABCD is a cyclic quadrilateral, find #angle# BAD.
10.
In the figure below, ABCD is a cyclic quadrilateral and BD is a diagonal. EADF is a straight line, #angle# CDF=#68^0#,#angle# BDC=#45^0# and #angle# BAE=#98^0#. Calculate the size of (a)# angle#ABD (b)#angle# CBD
11.
In the figure below AOC is a diameter of the circle centre O, AB=BC and #angle# ACD=#25^0#, EBF is a tangent to the circle at B. G is the point on the minor arc CD. (a) Calculate the size (i) #angle# BAD (ii) The obtuse #angle# BOD (iii) #angle# BGD (b) Show that #angle#ABE=#angle# CBF
12.
In the figure below, PQR is the tangent to the circle at Q. TS is a diameter and TSR and QUV are straight lines. QS is parallel to TV. Angle SQR=#40^0# and angle TQV=#55^0#. Find the following angles, giving reasons for each answer: (a) QTS (b) QRS (c) QVT (d) UTV
13.
In the figure below, QOT is a diameter, #angle# QTP=#48^0#, #angle# TQR=#76^0# and #angle# SRT=#37^0#. Calculate (a) #angle# RST (b) #angle# SUT (c) Obtuse #angle# ROT (d) #angle# PST
14.
ABCD is a cyclic quadrilateral and AB is a diameter. Angle ADC=#117^0#. Giving reasons for each step, calculate #angle# BAC
15.
The figure below shows two circles ABPQ and ABSR intersecting at A and B. PBS, QART and ABU are straight lines. The line UST is a tangent to the circle ABSR at S. #angle# BPQ=#80^0#, #angle# PBU=#115^0# and #angle# BUS=#70^0#. Find the values of the following angles, stating your reasons in each case. (a) #angle# BAR (b) #angle# STR (c) #angle# BSU (d) #angle# BRS
16.
On the figure below lines ABC and DC are tangents to the circle at B and D respectively. #angle# ACD=#40^0# and #angle# ABE=#60^0#. Giving reasons find the size of (a) CBD (b) CDE
17.
The diagram below shows a circle ABCDE. The line FEG is a tangent to the circle at point E. Line DE is parallel to CG, #angle# DEC=#28^0# and #angle#AGE=#32^0#. Calculate: (a) #angle# AEG (b) #angle# ABC
18.
In the figure below, O is the centre of the circle ABCD and AOD is a straight line. If AB=BC and angle DAC=#40^0#, calculate angle BAC.
19.
In the figure below, K,L,M and M are points on the circumference of a circle centre O. The points K,O,M and P are on a straight line. PN is a tangent to the circle at N. Angle KOL=#130^0# and angle MKN=#40^0#. Find the values of the following angles, stating the reasons in each case: (a) #angle# MLN (b) #angle# OLN (c) #angle# LNP (d) #angle# MPN
20.
In the figure below R,T and S are points on a circle centre O. PQ is tangent to the circle at T, POR is a straight line and #angle# QPR=#20^0#. Find the size of #angle# RST
21.
In the figure below, O is the centre of the circle passes through the points T, C and D. Line TC is parallel to OD and line ATB is a tangent to the circle at T. Angle DOC=#36^0#. Calculate the size of angle CTB
22.
In the figure below P, Q, R and S are points on the circle centre O. PRT and USTV are straight lines. Line UV is a tangent to the circle at S, #angle #RST=#50^0# and #angle# RTV=#150^0#. (a) Calculate the size of: (i) #angle# ORS (ii) #angle# USP (iii) #angle# PQR (b) Given that RT=7 cm and ST=9 cm, calculate to 3 significant figures: (i)the length of line PR (ii)the radius of the circle
23.
In the figure below, ABCD is a cyclic quadrilateral. Point O is the centre of the circle. Angle ABO =#30^0# and angle ADO =#40^0#. Calculate the size of angle BCD
24.
In the figure below, PR is a diameter of the circle centre O. Points P,Q, R and S on the circumference of the circle. Angle PRQ=#72^0#, QS=QP and line USV is a tangent to the circle at S Giving reasons, calculate the size of: (a) #angle#QPR (b) #angle# PQS (c) #angle# OQS (d) #angle# RTS (e) #angle# RSV
25.
In the figure below, BOD is the diameter of the circle centre O. Angle ABD =#30^0# and angle AXD=#70^0#. Determine the size of: (a)reflex angle BOC (b)angle ACO
26.
In the figure below, O is the centre of the circle. A, B, C and D are points on the circumference of the circle. Line AB is parallel to line DC and angle ADC=#55^0#. Determine the size of angle ACB.
27.
In the figure below, PQRS is a cyclic quadrilateral. PQ=QR, #angle# PQR=#105^0# and PS is parallel to QR. Determine the size of: (a) #angle# PSR (b) #angle# PQS
28.
An arc of a circle subtends an angle of #150^0# at the circumference of the circle. Calculate the angle subtended by the same arc at the centre of the circle.
29.
In the figure below, O is the centre of the circle, CO is the parallel to BA and #angle# AOB =#96^0#. Calculate #angle# CAO
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