Circles Test - ...

In the given figure with centre O, AOB = 30° and ∠BOC = 54°. Find ABC.

In the given figure, O is the centre of the circle. Find the measure of ABC.

In the given figure, a quadrilateral is inscribed in the circle. If ∠ADC = 55°, ∠ABD = 65°, ∠BAD = 85°, then find the value of ∠BDC & ∠BCD.

In the given figure, find the value of y when P is the centre of the circle.

What is the measure of angle PRS, if SQ is the diameter of the circle with centre O?

In the following figure, ABO = 43° and OA and OB are the radii of the cirlce. Find the measure of angle ADB.

In the given figure, if ABCD is a cyclic quadrilateral with respective angles, then what will be the value of x - y?

In the given figure, PQRS is a cyclic quadrilateral and ∠PQW is 145°. What is the measure of a° + b° + c° if ∠PRS is two fifth of ∠PSU?

What is the measure of ∠ADC in the given figure?

There is a circle which has a diameter PQ = 34 cm. A chord which is equal to 16 cm, has been drawn from point P to point Y. Find the least distance between centre of circle and the chord of circle.

In the given circle with centre O, ∠CBA = 50° and ∠ACB = 25°. Find ∠ODB.

In the given figure, EFHG is a cyclic quadrilateral such that ∠EFG = 50° and ∠FHE = 60°. Find the measure of ∠FEG.

In the given figure, O is the centre of the circle with chords AP and BP being produced to R and Q respectively. If ∠QPR = 55°, find the measure of ∠AOB.

In the given figure with centre O, if ∠OPQ = 58°, find the measure of x.

In figure, PQSR is a cyclic quadrilateral in which PQ is extended till F and QE || RS. If ∠FQE = 18° and ∠RPQ = 97°, find ∠PRS.

In the given figure, AB is the diameter and the chord CD is parallel to AB. Find the measure of CEB when BCD = 40°.

If AP = PB and O is the centre of the circle with AC as a straight line, find the value of x + y.

In the given figure, O is the centre of the circle and AOC = 120°. Find the value of 2x + y.

In the given figure with centre O, find ∠PQR, if AO = OB and ∠QPR = 40°.

In the given figure, find the measure of ∠XOZ, if ΔXYZ is an equilateral triangle and XYZO is a cyclic quadrilateral.

Fill in the blanks.

(a) A chord that passes through the centre of a circle is called a ____X_____, and is the longest chord.
(b) A __Y____ of a circle is a straight line segment whose endpoints both lie on the circle.
(c) Central angles subtended by arcs of the same length are __Z___.

In the given figure, O is the centre of smaller circle with a chord AB where AC = CB. Find ∠SRQ and ∠RSP.

In the given figure, O is the centre of the circle with AB as diameter. Which of the following statements is incorrect?

State 'T' for true and 'F' for false.
(i) The angle subtended by an arc at the centre is half the angle subtended by it at any point on the remaining part of the circle.
(ii) In a circle, an angle between a tangent and a chord from the point where they meet is double the angle in the alternate segment.
(iii) Two tangents drawn on a circle from a point outside are equal in length.

In the given circle with centre O, find ∠ABC if ∠OCB = 55° and AB = AC.