1. Division of line segment in a given ratio: We have to divide a line segment internally in the given ratio , where m and n are both positive integers.
2. Construction of similar triangles with given scale factor: In this, we are first required to construct a triangle with given dimensions and then construct a similar triangle with given scale factor. Scale factor (m + n) is the ratio of the sides of the triangle to be constructed with the corresponding sides of the given triangle.

• If m/n<1, then triangle to be constructed would be smaller than given triangle.
• If m/n>1, then triangle to be constructed would be greater than given triangle

The construction of first triangle with given dimensions has been covered in previous standards.

3. Construction of tangents to a circle: In this, we are required to construct the tangents from a point outside the circle.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 you could proceed as above.