2 A chord of a circle is equal to the radius of the
circle. Find the angle subtended by the chord at
on the minor

2 A chord of a circle is equal to the radius of the
circle. Find the angle subtended by the chord at
on the minor arc and also at a point on the
100
a point
major arc.
P
R
3. In Fig. 10.37, ZPQR = 100°, where P, Q and Rare
points on a circle with centre O. Find Z OPR.
Fig. 10.37
D
al angle
4. In Fig. 10.38, Z ABC = 69°, Z ACB = 31°, find
ZBDC.
D
69°
31°
B
C
Fig. 10.38
D
5. In Fig. 10.39, A, B, C and D are four points on a
circle. AC and BD intersect at a point E such
that Z BEC = 130° and Z ECD = 20°. Find
ZBAC.
20
B
AC С
60°
Fig. 10.39
6. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. IF ZDBC = 70°,
ZBAC is 30°, find BCD. Further, if AB=BC, find ECD.
1. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of
the quadrilateral, prove that it is a rectangle.
8. If the non-parallel sides of a trapezium are equal, prove that it is cyclic.​