Question The diagram shows a semicircle ACB with centre O and radius . Arc OC is part of a circle with centre A. (i)Express angle CAO in radians in terms of . (ii)Find the area of the shaded region in terms of , and , simplifying your answer. Solution (i) We are required to […]
Question The diagram shows a circle with centre O and radius cm. Points A and B lie on the circle and angle radians. The tangents to the circle at A and B meet at T. i. Express the perimeter of the shaded region in terms of and . ii. In the case where […]
Question The diagram shows a sector OAC of a circle with centre O. Tangents AB and CB to the circle meet at B. The arc AC is of length 6 cm and angle radians. i. Find the length of OA correct to 4 significant figures. ii. Find the perimeter of the shaded region. iii. […]
Question The diagram shows triangle ABC which is right-angled at A. Angle radians and AC = 8 cm. The points D and E lie on BC and BA respectively. The sector ADE is part of a circle with centre A and is such that BDC is the tangent to the arc DE at D. i. […]
Question The diagram shows a semicircle with diameter AB, centre O and radius r. The point C lies on the circumference and angle AOC = radians. The perimeter of sector BOC is twice the perimeter of sector AOC. Find the value of correct to 2 significant figures. Solution We are required to find the value […]
Question A sector of a circle of radius cm has an area of cm2. Express the perimeter of the sector in terms of and . Solution We are given that for the circular sector; We are required to find expression for perimeter of the circular sector. Expression for perimeter of a circular sector with radius […]
Question In the diagram, CXD is a semicircle of radius 7 cm with centre A and diameter CD. The straight line YABX is perpendicular to CD, and the arc CYD is part of a circle with centre B and radius 8 cm. Find the total area of the region enclosed by the two arcs. Solution […]