Use ruler and compass only for answering the question. Draw a circle of radius 4 cm . Mark the centre as O . Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P . Measure and write down the length of any one tangent.

Given, a circle of radius 4 cm and distance between the point and centre of a circle is 7 cm . Steps of construction: 1 . Draw a circle with centre O and with radius 4 cm . Take a point P outside the circle at a distance of 7 cm from its centre. Join OP . 2 . Using your ruler and compass draw a perpendicular bisector of OP , which intersects OP at (the mid-point) M . 3 . Taking M as centre and OM = MP = 7 2 = 3 . 5 cm as radius, draw a dotted circle, which intersects the given circle at Q and Q ' . 4 . Join PQ and PQ ' , which are the required tangents. On measuring the length of the tangent with the help of a ruler, we get PQ = PQ ' = 5 . 7 cm .

Using ruler and compass only, construct a ∆ A B C such that B C = 5 cm and A B = 6 . 5 cm and ∠ A B C = 120 ° . Construct a cyclic quadrilateral A B C D , such that D is equidistant from A B and B C .

Given: B C = 5 cm , A B = 6 . 5 cm and ∠ A B C = 120 ° Method to construct ∆ A B C and circumcircle of the triangle: i) A line segment B C = 5 cm is drawn. ii) From B , draw an angle 120 ° with B C . Let, ∠ X B C = 120 ° . iii) Cut an arc of radius 6 . 5 cm on the ray B X . Let, the arc intersects B X at A . iv) Now, A C is joined. ∴ ∆ A B C is the required triangle. v) The perpendicular bisectors of A B and B C to meet at point O . vi) With O as centre and radius O A , draw a circle. The circle will circumscribe ∆ A B C . Method to draw the cyclic quadrilateral A B C D , such that D is equidistant from A B and B C . i) Draw the angle bisector of ∠ A B C . Any point on the angle bisector of ∠ A B C is equidistant from A B and B C . ii) The point at which the angle bisector meets the circle named as D . Using ruler, A D and C D are joined. So, A B C D is the required cyclic quadrilateral. Hence, the above diagram shows the construction of cyclic quadrilateral A B C D .