NCERT Exemplar Problems – Class 10 Mathematics

1. To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that \(\angle BAX\) is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is

2. To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that \(\angle BAX\) is an acute angle and then points \(A_1, A_2, A_3, \ldots\) are located at equal distances on the ray AX and the point B is joined to

3. To divide a line segment AB in the ratio 5:6, draw a ray AX such that \(\angle BAX\) is an acute angle, then draw a ray BY parallel to AX and the points \(A_1, A_2, A_3, \ldots\) and \(B_1, B_2, B_3, \ldots\) are located at equal distances on ray AX and BY, respectively. Then the points joined are

4. To construct a triangle similar to a given \(\triangle ABC\) with its sides \(\dfrac{3}{7}\) of the corresponding sides of \(\triangle ABC\), first draw a ray BX such that \(\angle CBX\) is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points \(B_1, B_2, B_3, \ldots\) on BX at equal distances and next step is to join

5. To construct a triangle similar to a given \(\triangle ABC\) with its sides \(\dfrac{8}{5}\) of the corresponding sides of \(\triangle ABC\) draw a ray BX such that \(\angle CBX\) is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is

6. To draw a pair of tangents to a circle which are inclined to each other at an angle of \(60^\circ\), it is required to draw tangents at end points of those two radii of the circle, the angle between them should be