The path traced by the tip of the second's hand is a

The shape of the coin of RS 1 is

The wheels of a vehicle are in

The longest chord of a circle is called

The centre of a circle lies

Equal chords of a circle subtend equal angles at

In the following figure, 0 is the centre of the circle. \(\angle BAC=30°\). Then, the measure of \(\angle ADC\) is

In the given figure, O is the centre of the circle. ABCD is a trapezium in which AB || DC and \(\angle ADC=110°\) The measure of \(\angle ADC\) is equal to:

In the given figure, if ㄥPOR is 110, then find the value of ㄥPQR.

The sum of the opposite angles of a cyclic quadrilateral is : ___________.

In the figure, quadrilateral PQRS is cyclic. If ㄥP=80°, then R is equal to __________

Figure,O is centre of the circle and PA=PB Find ㄥOPA

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.

Find the length of a chord of a circle which is at a distance of 4 cm from the centre of the circle with radius 5 cm.

ABCD Is a cyclic quadrilateral. O is the centre of the circle. If \(\angle BOD=160°\), find \(\angle BPD\) .

In the figure, \(\angle AOB= 90°\)  and, \(\angle ABC= 30°\) then find the measure of  \(\angle CAO\).

In figure, O is the centre of the circle. If \(\angle AOB= 80°\). then find the measures of \(\angle ABD\) and \(\angle ACB\) .

(i) The centre of a circle lies in __________ of the circle. (exterior/interior).
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in___________ of the circle. (exterior/interior).
(iii) The longest chord of circle is a ________ of the circle.
(iv) An arc is a _____________ when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and __________ of the circle.
(vi) A circle divides the plane, on which it lies, ___________ parts.

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

ABCD is a cyclic quadrilateral whose diagonals intersect at E. If \(\angle\)DBC = 70°, \(\angle\)BAC = 30°, find \(\angle\)BCD. Further, if AB = BC, find \(\angle\)ECD.

PQRS is a trapezium with PQ || SR and PS = QR. Prove that the trapezium is cyclic.

D and E are points on equal sides AB and AC of isosceles \(\triangle\)ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.

Prove that the quadrilateral formed by internal angle bisectors of any quadrilateral is cylic.