Describe the process of drawing one tangent to a circle from an external point.

Draw a circle of radius 4 cm. Draw a tangent on this circle from an external point at a distance 9 cm from the centre of the circle.

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

If two tangents are drawn to a circle from a point outside it, then prove that the line segments joining the point of contact and the exterior point are equal and they subtend equal angles at the centre.

State True/False: “The equal chords of a circle are at equal distances from the centre of the circle.”

Write a difference between the geometric angle and trigonometrical angle.

Find the value of angle in degree made by the tangent of a circle with the radius of that circle at the point of contact

Find the mean proportion of xy² and xz²

The ratio of portion of profit of two friends is 1/2 : 1/3. Find the ratio of their capitals

The age of 100 persons present in a workshop is given in the following table. Find the average age of 100 people (by any method): Age Group Number of People 10 - 20 8 20 - 30 12 30 - 40 20 40 - 50 22 50 - 60 18 60 - 70 20

O is the circumcentre of the triangle ABC. OD ⊥ BC. Prove that ∠BOD = ∠BAC.

Solve: + = 2, (x ≠ -3, 3)