Question In the diagram, OADC is a sector of a circle with centre O and radius 3 cm. AB and CB are tangents to the circle and angle radians. Find, giving your answer in terms of and , i. the perimeter of the shaded region, ii. the area of the shaded region. Solution i. It is evident […]
Question The diagram shows a triangle AOB in which OA is 12 cm, OB is 5 cm and angle AOB is a right angle. Point P lies on AB and OP is an arc of a circle with centre A. Point Q lies on AB and OQ is an arc of a circle with centre B. […]
Question In the diagram, AB is an arc of a circle with centre O and radius 4 cm. Angle AOB is radians. The point D on OB is such that AD is perpendicular to OB. The arc DC, with centre O, meets OA at C. i. Find an expression in terms of for the perimeter of the shaded region […]
Question The diagram shows part of a circle with centre O and radius 6 cm. The chord AB is such that angle AOB = 2.2 radians. Calculate i. the perimeter of the shaded region, ii. the ratio of the area of the shaded region to the area of the triangle AOB, giving your answer in the form k : 1. Solution […]
Question The diagram shows a sector of a circle with radius cm and centre . The chord AB divides the sector into a triangle AOB and a segment AXB. Angle AOB is radians. i. In the case where the areas of the triangle AOB and the segment AXB are equal, find the value of the constant for which . ii. […]
Question The diagram shows triangle ABC in which AB is perpendicular to BC. The length of AB is 4 cm and angle CAB is radians. The arc DE with centre A and radius 2 cm meets AC at D and AB at E. Find, in terms of, i. the area of the shaded region, ii. the perimeter […]