#### To draw the circumcircle of a triangle, we need ____.

Perpendicular bisectors of sides are concurrent. Taking this concurrent point as centre we draw the circumcircle.

#### Any point on the perpendicular bisector of a line is equidistant from the end points of that line.

Any point on the perpendicular bisector of a line is equidistant from the end points of that line.

#### The number of circles can be drawn through three collinear points is ____.

When three points are collinear, no circle passes through them.

#### The bisector of an angle divides that angle in two equal halves.

The bisector of an angle divides the angle in two equal halves.

#### The following are the steps of construction of triangle ABC in which QR =10 cm, ∠Q = 70° and ∠R = 40°. 1. Draw the base line of 10 cm 2. Draw a line at 40° at the other end of the line 3. The intersection of the lines is the third point of the triangle 4. Use the protractor to draw a line at 70° to one end of the line The proper order of the steps for construction is ____.

Given, QR = 10 cm, ∠Q = 70° and ∠R = 30° Draw the base line of 10 cm Use the protractor to draw a line at 70° to one end of the line Draw a line at 40° at the other end of the line The intersection of the lines is the third point of the triangle. Hence, the correct order of steps for construction is 1, 4, 2 and 3.

#### The following are the steps for construction of triangle PQR in which QR = 11 cm, PQ = 6 cm and PR = 10 cm. 1. Draw a similar arc with compass set at 6 cm and with and with Q at the centre q 2. Draw the base line QR of length 11 cm 3. Set the compass so that the pencil and point are 10 cm apart, then draw an arc with point of the compass at P the proper order of steps for construction is ____.

Given QR = 11 cm, PQ = 6 cm and PR = 10 cm Draw the base line QR of length 11 cm Set the compass so that the pencil and point are 10 cm apart, and then draw an arc with point of the compass at P Draw a similar arc with compass set at 6 cm and with Q at the centre The point where the two arcs cross is the third corner of the triangle Hence, the required steps of construction are 2, 3 and 1

#### If a circle is drawn passing through all the vertices of a square, then it is ____.

Circle passing through vertices is circumcircle.

#### The following are the steps of construction of a triangle ABC in which AB= 9 cm, ∠A = 40° and ∠B = 70°. 1. Use a protractor to draw an angle of 70° at B. 2. Draw AB of length 9 cm. 3. Extend the lines until they intersect each other at C to form a triangle. 4. Draw an angle of 40° at A. The proper order of steps of construction is ____.

Given AB= 9 cm, ∠A = 40° and ∠B = 70° Draw AB of length 9 cm Use a protractor to draw an angle of 70° at B. Draw an angle of 40° at A. Extend the lines until they intersect each other at C to form a triangle Hence, the correct order of steps of construction is 2, 1, 4 and 3.

#### With two given points as centres and radius more than half of their distance, two arcs are drawn to cut each other at either side of the segment joining them. Line joining these two intersection points is perpendicular bisector of the segment joining the given points.

With two given points as centres and radius more than half of their distance, two arcs are drawn to cut each other at either side of the segment joining them. Line joining these two intersection points is perpendicular bisector of the segment joining the given points.