9th Class Mathematics Circles Question Bank Circles

Two circles intersect at two points A and B. If AD and AC are diameters of the circles, then which of the following step is INCORRECT in order to prove that B lies on the line segment DC?

(p) Join AB.

(q)\[\angle ABC={{90}^{o}}\]and\[\angle ABC={{90}^{o}}\](Angle in semicircle)

(r)\[\angle ABD+\angle ABC={{360}^{o}}\]

(s) DBC is a straight line segment. Hence B lies on the line segment DC.

A)           p

B)        q

C)                    r

D)        s

Correct Answer: C

Solution :

(r) is incorrect. The correct step should be \[\angle ABD+\angle ABC={{180}^{o}},\]for DBC to be a straight line segment