Question

Two circle intersect at A and B AC andAD are diameters of circle proveC. B andD are colinear points

Answer 1

Step-by-step explanation:

Given: c1 and c2 are two circles with AD and AC as their diameters respectivey

To prove : D, B and C are colinear( B lies on CD) I.e, ANGLE. DBC = 180°

Construction: Join AB

Proof: In c1,

arc ABD is a semicircle

so, ANGLE. ABD = 90° ( ANGLE OF A SEMICIRCLE IS 90°)

Similary, in c2 arc ABC is a semicircle so ANGLE. ABC is 90° ( ANGLE OF A SEMICIRCLE IS 90°)

NOW, ANGLE ABD + ANGLE ABC

= 90° + 90°

= 180°

Since the sum of these two angles is 180°, this means they are linear pair and linear pair occurs only on a straight line.

Therefore, C, B and D are colinear