Question 11: In the following figure, is the center and is equilateral. Find (i) (ii)

Answer:

In , since it is equilateral, all angles are equal.

(angles int he same segment)

Since is a cyclic quadrilateral

Question 12: Given: and . Find the value of .

Answer:

(angles in same segment)

Let (angles in same segment)

Let

Question 13: is a cyclic quadrilateral in circle with center . If ; find .

Answer:

(angle in the semi circle)

Question 14: In the given figure, is a diameter of the circle and . Find .

Answer:

(radius of the same circle)

Therefore in

(angle in the same segment)

Question 15: In the following figure, is the center of the circle, and . Find .

Answer:

Let

Hence

Question 16: is a cyclic quadrilateral in which and . Calculate (i) (ii) (iii)

Answer:

(i)

(ii)

is a cyclic quadrilateral

Question 17: In the figure given below, is the diameter of the circle whose center is . Given that: . Show that .

Answer:

In

(radius of the same circle)

Hence

Question 18: In the figure given below, and are straight lines through the center of the circle. If and find (i) (ii)

Answer:

(angle in a semi circle)

(i) Therefore

Question 19: In the given figure, is a diameter of a circle whose center is . A circle is described on as a diameter. is a chord of the larger circle intersects the smaller circle at . Prove .

Answer:

(angles in a semi circle)

(common angle)

Hence

Question 20: In the following figure, (i) if , find and . (ii) Prove that is parallel to .

Answer:

(i) is a cyclic quardilateral

(ii) Since