Chapter 17 - Circles Exercise Ex. 17(B)

Question 1

In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal.

Prove it.

Solution 1

 

Question 2

In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If DEF = 110^, calculate :

(i) AFE,(ii) FAB.

Solution 2

Question 3

If two sides of a cycli-quadrilateral are parallel; prove thet:

(i) its other two side are equal.

(ii) its diagonals are equal.

Solution 3

 

Question 4

The given figure show a circle with centre O. also, PQ = QR = RS and PTS = 75°. Calculate:

(i) POS,

(ii) QOR,

(iii) PQR.

Solution 4

 

Question 5

In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of :

(i) AOB,

(ii) ACB,

(iii) ABC.

Solution 5

Question 6

In a regular pentagon ABCDE, inscribed in a circle; find ratio between angle EDA and angel ADC.

Solution 6

Question 7

In the given figure. AB = BC = CD and ABC = 132° calculate:

(i) AEB,

(ii) AED,

(iii) COD.

Solution 7

 

Question 8

In the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108° find :

(i) CAB,

(ii) ADB.

Solution 8

 

Question 9

The figure shows a circle with centre O. AB is the side of regular pentagon and AC is the side of regular hexagon. Find the angles of triangle ABC.

Solution 9

Question 10

In the given figire, BD is a side of a regularhexagon, DC is a side of a regular pentagon and AD is adiameter. Calculate:

(i) ADC,

(ii) BAD,

(iii) ABC,

(iv) AEC.

Solution 10