Circular Measures

Question 9: In diagram 5, AOBDE, is a semicircle with centre O and has radius of 5cm. ABC is a right angle triangle. It is given that AD DC =3.85 and DC=2.31 cm.   [Use π = 3.142] Calculate (a) the value of θ, in radians,   [2 marks] (b) the perimeter, in cm, of the segment ADE,    … Read more

Question 7:Diagram below shows a semicircle PTS, centre O and radius 8 cm. PTR is a sector of a circle with centre P and Q is the midpoint of OS.[Use π = 3.142]Calculate(a) ∠TOQ, in radians,(b) the length , in cm , of the arc TR ,(c) the area, in cm2 ,of the shaded region.Solution: … Read more

Question 5: Diagram below shows a circle PQRT, centre O and radius 5 cm. AQB is a tangent to the circle at Q. The straight lines, AO and BO, intersect the circle at P and R respectively.  OPQR is a rhombus. ACB is an arc of a circle at centre O. Calculate (a) the angle x , in … Read more

Question 3: Diagram below shows two circles. The larger circle has centre A and radius 20 cm. The smaller circle has centre B and radius 12 cm. The circles touch at point R. The straight line PQ is a common tangent to the circles at point P and point Q. [Use π = 3.142] Given that angle PAR … Read more

Question 1: Diagram shows a circle, centre O and radius 8 cm inscribed in a sector SPT of a circle at centre P.  The straight lines, SP and TP, are tangents to the circle at point Q and point R, respectively. [Use p= 3.142] Calculate (a) the length, in cm, of the arc ST, (b) … Read more

Question 4: Diagram below shows a circle with centre O. The length of the minor arc is 16 cm and the angle of the major sector AOB is 290o. Using  π = 3.142, find (a) the value of  θ, in radians. (Give your answer correct to four significant figures) (b) the length, in cm, of the … Read more

Question 1: The figure shows the sector OCB of radius 13 cm at the centre O. The length of the arc CB = 5.2 cm. Find (a) the angle in radians, (b) the perimeter of the shaded region. Solution: (a) s = r θ 5.2 = 13 ( ∠ C O B ) ∠ C O … Read more

1.3 Area of a Sector of a Circle (A) Area of a Sector of a Circle 1. If a circle divided into two sectors of different sizes, the smaller sector is known as the minor sector while the larger sector is known as the major sector. 2. If AOB is the area of a sector … Read more

(A) Formulae for Length and Area of a Circle r = radius, A= area, s = arc length, q = angle, l = length of chord (B) Length of an Arc of a Circle Example 1: An arc, AB, of a circle of radius 5 cm subtends an angle of 1.5 radians at the centre. … Read more

8.1 Radians (A) Terminology: (B) Convert degrees to radians: (C) Convert radians to degrees: