NCERT Solutions for Class 10 Maths Chapter 11- Constructions

Constructions are generally done with a ruler and compass. The Maths chapter 11 Constructions discusses how to divide the line segment into a given ratio, construction of triangles using scale factor, construction of tangent to a circle. The line segment divides in a proportional ratio, and it is proved by Thales theorem, which is also known as the Basic Proportionality theorem. The similar triangles or quadrilateral have their corresponding angles equal and sides in the same ratio. Angles in alternate segments are equal.

Bisecting a line segment:

STEP 1: With a radius of more than half the length of the line segment, draw arcs centred at one end of the line so that they intersect at the other side of the line segment.

STEP 2: Join the points of intersection.

Maths Chapter 11 Constructions further deals with drawing tangents to a circle. A tangent to a circle is a line that meets the circle at only one point. For every point on the circle, there is a tangent passing through it. If the point in an interior region of the circle, the line through that point is secant, so there is no tangent to the circle. When the point lies on the circle, there is one tangent to the circle. When the point lies outside of the circle, there are two tangents to the circle.

Consider C as a circle, with O as a centre and point P outside. Join PO. Let M be the midpoint of PO. Keeping as the midpoint, join PO and draw bisector to it. Then draw a circle by taking M as centre and MO as radius, intersect the given circle. Now join PQ and PR as tangents. Therefore, we can draw two tangents using point outside the circle.