Draw a right-angled triangle having two sides 4 cm and 8 cm length respectively, containing the right angle. Then draw the circumcircle of the right-angled triangle. (Only traces of construction are required.)

Draw a triangle whose sides are of lengths 6 cm, 8 cm, and 10 cm. Draw the incircle of this triangle.

Draw a right-angled triangle of which two sides containing the right angle have the lengths 5 cm and 6 cm. Now draw an incircle of the triangle.

Draw a right angled triangle whose two adjacent sides of the right angle are 4 cm and 5 cm. Construct the circumcircle of this triangle

Describe the process of drawing an incircle of a right-angled triangle.

Distance between two pillars is 150 m, height of one pillar is three times the other pillar. From the mid-point of the line joining their foot the angles of elevation of the top of the two pillars are complementary. Find the height of the smaller pillar

From the middle of a ground Habu observes a flying bird toward north at an angle of elevation 30°, after 2 minutes he observes the same bird at an angle of elevation 60° toward south. If the bird always flies in a straight line at height 50√3 meters from the ground level, find its velocity.

Find the value of 2√3 geometrically.

AB is the diameter of the circle with centre O. From a point P on the circle, a perpendicular PN is drawn on AB. Prove geometrically that PB² = AB.BN.

State and prove Pythagoras theorem.

Prove that in a cyclic quadrilateral opposite angles are supplementary.

Divide ₹ 21,866 into two parts such that the amount of the first part for 3 years and amount of the second part for 5 years are equal at the same rate of 5% compound interest.