#### Concentric circles are circles with a common centre and different radii.

Concentric circles are circles with a common centre and different radii.

#### Arrange the following steps in correct order to construct a regular hexagon in a circle: i) Mark OA = AB = BC = CD = DE = EF. ii) Join AB, BC, CD, DE, EF and FA. iii) ABCDE is a regular hexagon.

i, ii and iii is the correct sequence of steps to construct a regular hexagon in a circle.

#### To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is

The angle between a pair of tangents to a circle which are inclined to each other at an angle is supplementary to the angle between the two radii of the circle. Thus, the angle between the radii of the circle = 180° - 35° = 145°

#### The points of intersection of direct common tangents to two circles divide the line joining centres respectively externally in the ratio of their ____.

The points of intersection of direct common tangents to two circles divide the line joining centres respectively externally in the ratio of their radii.

#### To draw a pair of tangents to a circle which are inclined to each other at an angle of 60^{o},it is required to draw tangents at the end points to those two radii of the side, the angle between which is

The angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the two radii drawn from the points of contact to the center. To draw a pair of tangents to a circle which are inclined to each other at an angle of 60^{o}, it is required to draw tangents at the end points to those two radii of the side, the angle between which is is 180° - 60°= 120^{o}.

#### If two circles are touching internally, then the number of common tangents can be drawn is ____.

The two circles are touching internally, then one common tangent can be drawn.

#### A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?

The radius of the circle is 6 cm and the point O lies at a distance of 10 cm from the centre. So, it is clear that the point O lies outside the circle. It is known that only two tangents can be drawn from a point lying outside the circle. Thus, two tangents can be drawn from the point O.

#### In drawing triangle ABC, it is given that AB = 3 cm, BC = 2 cm and AC = 6 cm. It is not possible to draw the triangle as:

We know that in a triangle, sum of two sides is greater than the third side. Here, AB + BC = 5 cm and AC = 6 cm so, we have: AC > AB + BC Thus, it is not possible to construct triangle ABC with given measurements.

#### Identify the incorrect statement.

All congruent figures are similar but all similar figures are not congruent.