Question The diagram shows a major arc AB of a circle with centre O and radius 6 cm. Points C and D on OA and OB respectively are such that the line AB is a tangent at E to the arc CED of a smaller circle also with centre O. Angle COD = 1.8 radians. i. Show that […]
Question The diagram shows a metal plate ABCD made from two parts. The part BCD is a semicircle. The part DAB is a segment of a circle with centre O and radius 10 cm. Angle BOD is 1.2 radians. i. Show that the radius of the semicircle is 5.646 cm, correct to 3 decimal places. ii. Find the perimeter of the […]
Question In the diagram OCA and ODB are radii of a circle with centre O and radius cm. Angle adians. CD and AB are arcs of circles with centre O and radii cm and cm respectively. The perimeter of the shaded region ABDC is 4.4r cm. i. Find the value of . ii. It is given that the area of […]
Question The diagram shows triangle ABC where AB=5cm, AC=4cm and BC=3cm. Three circles with centres at A, B and C have radii 3 cm, 2 cm and 1 cm respectively. The circles touch each other at points E, F and G, lying on AB, AC and BC respectively. Find the area of the shaded region EFG. Solution It is […]
Question The diagram shows a circle with radius r cm and centre O. The line PT is the tangent to the circle at P and angle radians. The line OT meets the circle at Q. i. Express the perimeter of the shaded region PQT in terms of r and . ii. In the case where and , find the area of […]
Question In the diagram, AOB is a quarter circle with centre O and radius r. The point C lies on the arc AB and the point D lies on OB. The line CD is parallel to AO and angle radians. i. Express the perimeter of the shaded region in terms of r, and . ii. For the case […]
Question a. Figure 1 In Fig. 1, OAB is a sector of a circle with centre O and radius r. AX is the tangent at A to the arc AB and angle . i. Show that angle . ii. Find the area of the shaded segment in terms of r and . b. Figure 2 […]