Page 2 - Worksheet 2 Ch.10 Circle

7 If A, B, C and D are four points such that BAC = 45° and BDC = 45°, then A, B, C 1
and D are concyclic or not?
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Section B
8 ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and 2
D. Prove that

CBD + CDB = ½ BAD.

9 O is the circumcentre of the ΔABC and D is the mid-point of the base BC. Prove that 2
BOD = A.

10 On a common hypotenuse AB, two right angled triangles, ACB and ADB are situated on 2
opposite sides. Prove that BAC = BDC.

Section C
11 Two chords AB and AC of a circle subtends angles equal to 90° and 150°, respectively 3
at the centre. Find BAC, if AB and AC lie on the opposite sides of the centre.

12 If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, 3
prove that the quadrilateral, so formed is cyclic.

13 The circumcentre of the ΔABC is o. Prove that OBC + BAC = 90°. 3

Section D
14 If two equal chords of a circle intersect, prove that the parts of one chord are separately 4
equal to the parts of the other chord

15 O is the centre of the circle, BD = OD and CD ⊥ AB. Find CAB. 4

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