 # Constructions

## Division of a Line Segment A line segment can be divided in a given ratio m:n (say) where both m and n are positive integers. There are two methods to construct the division of a line segment. The ratio of the sides of the triangles to be constructed with the corresponding sides of the given triangle is known as their scalar factor. Construction of a Triangle Similar to a given Triangle There are two cases while constructing a similar triangle: (i) To construct a triangle similar to a given triangle as per a given scale factor m/n where mm. Construction of Tangents to a Circle There are four cases while constructing tangents to a circle: (i) Given point on the circle and the centre of the circle is known. (ii) Given point on the circle and the centre of the circle is unknown. (iii) Given point outside to the circle and the centre of the circle is known. (iv) Given point outside to the circle and the centre of the circle is unknown. To find the centre of a circle, take any two non parallel chords of the circle and then find the point of intersection of their perpendicular bisectors. This point is the centre of the circle. After knowing the centre we proceed as per the case (iii).

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