Circles Test - ...

In the given circle, O is the centre and length of chord XY = length of chord ZW. If XOY = 60°, then what is the measure of ZOW?

In the given figure, AOB is a diameter of a circle with centre O. If BOD = 140°, then find the measure of ACD.

O is the centre of the circle as shown in the diagram. The distance between P and Q is 4 cm such that the line through P and Q passes through the centre O. The measure of ROQ is

In the given circle, O is the centre, AB = BC and OM = 5 units. The length of ON is equal to ____.

In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P. If DBC = 60° and BAC = 40°, find the measure of BCD.

In the given figure, O is the centre of the circle. What is the measure of ACB?

In the given circle, O is the centre and AB = CD. What is the measure of AOB?

In the given figure, O is the centre of the circle and AOC = 112°. Find the measure of ABC.

In the following figure, O is the centre of the circle and ∠AOB = 88°. What is the measure of ∠OCB?

In the given figure, O is the centre of the circle, AOB = POQ = 30° and XOY = ZOW = 40°. Also, XY = 4 units and AB = 3.5 units. The value of (AB + ZW + PQ + XY) is

In the given figure, O is the centre of the circle and CBD = 56°. Find the measure of AEC.

If in the given figure, O is the centre of the circle and AEB + ACB + ADB = 3x, then find the measure of AOB.

In the given figure, O is the centre of the circle and AE is a diameter. If AB = BC and BFC = 25°, find the value of ABC.

Consider the figure:



If x = 60° and y = 120°, then (w - z) is equal to

In the given figure, O is the centre of the circle.


If CBN = 74°, then AOC is equal to

In the given figure, O is the centre and m AOC = 130°. Then, m CBE is equal to

What is the length of PN, if AB = 30, PM = 8, DC = 16 and P is the centre of the circle?

In the given figure, O is the centre of the circle, ST = UV, SV is a straight line and SOT = 85°. The measure of UOT is

In the following figure, AC is diameter of the circle. AB = BC and AED = 135°. Find the values of DEC and BAD.

In the given figure, AB is the diameter of the circle. C and D lie on the semi-circle. If ABC = 65° and CAD = 45°, DCA equals

In the given figure, chord ED is parallel to the diameter AC of the circle. If CBE = 65°, then what is the value of DEC?

Fill in the blanks with the help of the given table.

(i) If two arcs are P , then their corresponding chords are Q .
(ii) The minimum number of points required to draw a circle is R .
(iii) If one side of a cyclic quadrilateral is produced, then the exterior angle so formed is equal to the S .

State 'T' for true and 'F' for false for the following statements.

(i) The region between an arc and the two radii, joining the centre to the end points of the arc is called a segment.
(ii) The length of a complete circle is called diameter.
(iii) For a given chord, the area of the major segment is always equal to the area of the minor segment.
(iv) From any two given points, one can draw infinite number of circles passing through them.

In the given figure, ABCD is a cyclic quadrilateral. A circle passing through the points A and B meets AD and BC at points E and F, respectively. Which of the given statements is/are true for the given problem?



(i) EF DC
(ii) ∠1 = ∠2
(iii) ∠2 = ∠3
(iv) DC AB

In the given figure, AB is a diameter of the circle and CD is a chord equal to the radius of the circle. If AC and BD are extended and intersect at a point E, then which of the following steps is INCORRECT in order to prove that ∠AEB = 60°?



Step - 1: Join OC, OD and BC. Triangle ODC is an equilateral triangle.
Step - 2: ∠COD = 60°. Now, ∠CBD = 2∠COD (Angle subtended by an arc at the centre = 2 × Angle subtended by the arc at any point on the circle)
Step - 3: This gives ∠CBD = 30°.
Step - 4: ∠ACB = 90° (Angle subtended by a semi-circle)
Step - 5: So, ∠BCE = 180° – ∠ACB = 90°
Step - 6: ∠CEB = 90° – 30° = 60°, i.e. ∠AEB = 60°