Students' Learning Outcomes
After completing this unit, the students will be able to:
- Solve problems by using the tangent and angle properties of a circle:
- If a line is drawn perpendicular to a radial segment of a circle at its outer end point, it is tangent to the circle at that point.
- The tangent to a circle and the radial segment joining the point of contact and the centre are perpendicular to each other.
- The two tangents drawn to a circle from a point outside it, are equal in length.
- If two circles touch externally or internally, then the distance between their centres is respectively equal to the sum or difference of their radii.
- The measure of a central angle of a minor arc of a circle is double that of the angle subtended by the corresponding major arc.
- Any two angles in the same segment of a circle are equal.
- The angle in a semi-circle is a right angle, in a segment greater than a semi-circle is less than a right angle, in a segment less than a semi-circle is greater than a right angle.
- The opposite angles of any quadrilateral inscribed in a circle are supplementary.
- Find the arc length and area of sector of a circle using angle in both degrees and radians.
- Apply concepts of tangents and angles of a circle to real life world problems (such as architecture, monuments, pyramids).
- Apply trigonometry to solve real life problems in arc length and area of the sector of circle.