In this chapter, we will be learning about angles and tangents of circles. We will start by understanding the angle at the circumference and the central angle subtended by an arc. Next, we will explore the concept of cyclic quadrilaterals, which are quadrilaterals that can be inscribed in a circle. We will also study tangents to circles, which are lines that touch the circle at only one point. Finally, we will make and verify conjectures about the relationships between angles at the circumference and central angle subtended by particular arcs. We will use these relationships to determine the values of angles in circles and solve problems involving angles in circles.
• Make and verify conjectures about the relationships between (i) angles at the circumference, (ii) angles at the circumference and central angle subtended by particular arcs, and hence use the relationships to determine the values of angles in circles
• Solve problems involving angles in circles
• Recognise and describe cyclic quadrilaterals
• Make and verify conjectures about the relationships between angles of cyclic quadrilaterals, and hence use the relationships to determine the values of angles of cyclic quadrilaterals
• Solve problems involving cyclic quadrilaterals
• Recognise and describe the tangents to circles
• Make and verify conjectures about (i) the angle between tangent and radius of a circle at the point of tangency, (ii) the properties related to two tangents to a circle, (iii) the relationship of angle between tangent and chord with the angle in the alternate segment which is subtended by the chord, and hence perform the related calculations
• Solve problems involving tangents to circles
• Solve problems involving angles and tangents of circles
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