PRACTICE QUESTIONS WORKSHEET ON CIRCLES AND CYCLIC QUADRILATERAL

(1)  Find the value of x in the given figure. 

Solution

(2)  In the given figure, AC is the diameter of the circle with centre O. If <ADE = 30° ; <DAC = 35° and <CAB = 40°. Find (i) <ACD   (ii)  <ACB  (iii)  <DAE

Solution

(3)  Find all the angles of the given cyclic quadrilateral ABCD in the figure.

Solution

(4)  In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that <DBC = 40° and <BAC = 60° find

(i)  <CAD   (ii)  BCD

Solution

(5)  In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8cm and CD = 6cm. If OM ⊥ AB and OL ⊥ CD distance between LM is 7cm. Find the radius of the circle.

Solution

(6)  The arch of a bridge has dimensions as shown, where the arch measure 2 m at its highest point and its width is 6 m. What is the radius of the circle that contains the arch?

Solution

(7)  In figure, <ABC =120 , where A,B and C are points on the circle with centre O. Find <OAC ?

Solution

(8)  A school wants to conduct tree plantation programme. For this a teacher allotted a circle of radius 6m ground to nineth standard students for planting sapplings. Four students plant trees at the points A,B,C and D as shown in figure. Here AB = 8m, CD = 10m and AB is perpendicular to CD. If another student places a flower pot at the point P, the intersection of AB and CD, then find the distance from the centre to P.

Solution

(9)  In the given figure, <POQ = 100 and <PQR = 30, then find <RPO .

Solution

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