Topical Past Question On Circular Measure2
Topical Past Question On Circular Measure2
Topical Past Question On Circular Measure2
1.
Q4 Nov 2001
2. The diagram shows the circular cross-section of a uniform cylindrical log with centre
O and radius 20 cm. The points A, X and B lie on the circumference of the cross-
section and AB � 32 cm.
(i) Show that angle AOB �1.855 radians, correct to 3 decimal places. [2]
The section AXBCD, where ABCD is a rectangle with AD �18 cm, is removed.
(iii) Find the area of the new cross-section (shown shaded in the diagram). [3]
Q7 Jun 2002
3.
(i) Show that the area, A cm2, of the shaded region is given by A= .
[2]
(ii) In the case where _ 0.8 and r = 15, evaluate the length of the perimeter of the
shaded region.
Q3 Nov 2002
4.
The diagram shows a semicircle ABC with centre O and radius 8 cm. Angle AOB =
radians.
(i) In the case where = 1, calculate the area of the sector BOC. [3]
(ii) Find the value of for which the perimeter of sector AOB is one half of the
perimeter of sector BOC. [3]
(iii) In the case where , show that the exact length of the perimeter of triangle
ABC is (24 + 8 ) cm. [3]
Q9 Jun 2003
(iii) In the case where r = 8, find the length of the chord PQ. [3]
Q3 Nov 2003
Q5 Jun 2004
7. In the diagram, AC is an arc of a circle, centre O and radius 6 cm.
The line BC is perpendicular to OC and OAB is a straight line.
Q3 Nov 2004
8.
In the diagram, ABC is a semicircle, centre O and radius 9 cm. The line BD is
perpendicular to the diameter AC and angle AOB = 2.4 radians.
Q3 Jun 2005
9. In the diagram, OAB and OCD are radii of a circle, centre O and
radius 16 cm. Angle AOC = αradians. AC and BD are arcs of
circles, centre O and radii 10 cm and 16 cm respectively.
(i) In the case where α= 0.8, find the area of the shaded
region. [2]
(ii) Find the value of αfor which the perimeter of the shaded
region is 28.9 cm. [3]
Q3 Nov 2005
10.
The diagram shows a circle with centre O and radius 8 cm. Points A and B lie on the
circle. The tangents at A and B meet at the point T, and AT = BT = 15 cm.
(i) Show that angle AOB is 2.16 radians, correct to 3 significant figures. [3]
Q7 Jun 2006
11.
In the diagram, AOB is a sector of a circle with centre O and radius 12 cm. The point A
lies on the side CD of the rectangle OCDB. Angle AOB = radians. Express the
area of the shaded region in the form a( ) − b , stating the values of the integers a
and b. [6]
Q3 Nov 2006
12.
In the diagram, OAB is a sector of a circle with centre O and radius 12 cm. The lines
AX and BX are tangents to the circle at A and B respectively. Angle AOB =
radians.
(i) Find the exact length of AX, giving your answer in terms of . [2]
(ii) Find the area of the shaded region, giving your answer in terms of and .
[3]
Q5 Jun 2007
13.
In the diagram, AB is
an arc of a circle, centre O and radius r cm, and angle AOB = radians. The point X
lies on OB and AX is perpendicular to OB.
(i) Show that the area, A cm2, of the shaded region AXB is given by
[3]
(ii) In the case where r = 12 and = , find the perimeter of the shaded region
AXB, leaving your answer in terms of 3 and . [4]
Q7 Nov 2007
14.
The diagram shows a circle with centre O and radius 5 cm. The point P lies on the
circle, PT is a tangent to the circle and PT = 12 cm. The line OT cuts the circle at the
point Q.
Q3 Jun 2008
15.
In the diagram, the circle has centre O and radius 5 cm. The points P and Q lie on the
circle, and the arc length PQ is 9 cm. The tangents to the circle at P and Q meet at the
point T. Calculate
Q3 Nov 2008
16.
The diagram shows a circle with centre O. The circle is divided into two regions, R1
and R2 , by the radii OA and OB, where angle AOB = radians. The perimeter of the
region R1 is equal to the length of the major arc AB.
(ii) Given that the area of region R1 is 30 cm2, find the area of region R2 , correct to
3 significant figures. [4]
Q5 Jun 2009
17.
(i) Express in terms of r and show that the area, A cm2, of the sector is given by
(ii) Given that r can vary, find the stationary value of A and determine its nature. [4]
Q7 Nov 2009
18. The diagram shows a metal plate ABCDEF which has been made by removing the
two shaded regions from a circle of radius 10 cm and centre O. The parallel edges AB
and ED are both of length 12 cm.
(i) Show that angle DOE is 1.287 radians, correct to 4 significant figures. [2]
Q3 Jun 2010
19.
The diagram shows a rhombus ABCD. Points P and Q lie on the diagonal AC such
that BPD is an arc of a circle with centre C and BQD is an arc of a circle with centre
A. Each side of the rhombus has length 5 cm and angle BAD = 1.2 radians.