State True or False: If two chords of a circle are at an equal distance from the centre of that circle, then those two chords will be always parallel.

Two circles of diameter 5 cm and 7 cm touch each other internally, the distance between their centres will be - (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm

Prove that the perpendicular drawn to a chord which is not a diameter, from the center of the circle, bisects the chord.

The radius of the circle with the center 'O' is 13 cm and a chord AB with the length of 10 cm on it. Calculate the distance of the chord AB from the center of the circle.

Two chords, AB and CD of a circle with center O, when produced, intersect each other at the point P. Prove that ∠AOC−∠BOD = 2 × ∠BPC

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

Mode = 2 × Median – 3 × Mean.

If x be the volume, y be the area of the base and z be the height of a cone then the value of x / yz is 3.

ABCD is a cyclic quadrilateral. If ∠ADB = x° and ∠ABD = y° then ∠BCD is (x + y)°.

If the sum of the square of the roots of the equation 6x² + x + k = 0 is , then the value of k is 12.