The centre of a circle lies

Equal chords of a circle subtend equal angles at

Given a circle with centre O and smallest chord AB is of length 6 cm and the longest chord CD of the circle is of length 10 cm, then the radius of the circle is:

In figure, if OA = 5 cm, AB = 8 cm and OD丄AB then CD is equal to:

Equal chords of a circle are equidistant from

Find the length of a chord which is at a distance of 3 cm from the centre of a circle whose radius is 5 cm.

In the figure, O is the centre of the circle. Arc BCD subtends an angle of 140° at the centre. BC is produced to P and CD is joined. Find measure of \(\angle DCP\).

PQRS is a cyclic quadrilateral, in which \(\angle P=2x°\), \(\angle Q=y°\), \(\angle R=3x°\) and \(\angle S=2y°\). Find the values of x and y. 

ABCD is a cyclic quadrilateral in which AB II CD. If ㄥD=70, find all the remaining angles.

If a line intersects two concentric circles with common centre O, at A, B, C and D. Prove that AB = CD

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

In figure, \(\angle ABC=69°,\ \angle ACB=31°\), find \(\angle BDC\) .

If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

In the figure, diameter AB and a chord AC have a 'common end point A. If the length of AB is 20 cm and of AC is 12 cm, how far is AC from the centre of the circle?

Prove that the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Bisector AD of  \(\angle BAC\) of \(\Delta ABC\) passes through the centre O of the circumcircle of
\(\Delta ABC\) Prove that AB = AC.

Raja, Renu and Reena are three friends. They decided to sweep a circular park near their homes. They divided the park into three parts by two equal chords AB and AC for convenience.
(i) Prove that the centre of the park lies on the angle bisector of \(\angle\)BAC
(ii) Which mathematical concept is used in the above problem?
(iii) By deciding sweeping, which value is depicted by the three friends?

Mr. Mehta, owner of a biscuit manufacturing company, wants to stick butter on a circular biscuit, in the form of two equal chords. He wishes the length of each chord should be more than the radius and less than the diameter of the biscuit. Assuming
that the thickness of the biscuits is negligible.
(i) Prove that the butter-chords subtend equal angles at the centre of the biscuit.
(ii) What is the measure-range of the angle subtended by either butter-chord at the centre?
(iii) Which mathematical concept is used in the above problem?
(iv) Which value is depicted by Mr. Mehta as an owner of a manufacturing company?