This GSEB Class 10 Maths Notes Chapter 11 Constructions covers all the important topics and concepts as mentioned in the chapter.
Constructions Class 10 GSEB Notes
We have done certain constructions using a straight edge (ruler) and a compass, e.g. bisecting an angle, drawing the perpendicular-bisector of a line segment, some constructions of triangles etc. and also gave their justification. In this chapter, we shall study some more constructions by using the knowledge of earlier constructions you would also be expected to give the mathematical reasoning behind, why such constructions work.
Construction of Tangents
We know that if a point lies inside a circle, there cannot be a tangent to the circle through this point. However if a point lies on the circle, then there is only one tangent to the circle at this point and it is perpendicular to the radius through this point.
- Take a point on the circle.
- Join centre of circle and this point i.e. draw the radius of the circle through this point.
- Draw perpendicular to the radius through this point i.e. construct a right angle (90°) at this point. The perpendicular is the tangent to the circle through this point.
Note:
If centre of the circle is not given, you may locate its centre first by taking any two non-parallel chords and then finding the point of intersection of their perpendicular bisectors. Then follow the steps in steps to draw a tangent at a point on the circle.