Prove that the line joining mid points of 2 equal chords of a circle subtand equal angles with the chord 2 circles have AB as their common chord AC is diameter AD is diameter of second circle show B,C,D are collinear

1
by rajusetu
have a look at http://brainly.in/question/80610 also
it is urgent
hope so you u understand
have a look at http://brainly.in/question/80610
How do u know that I study in fiitjee.

2015-02-15T16:45:42+05:30

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
See diagram.

1st problem

the two chords must be adjacent. One point is common between two chords.  Then only it is true.  We take angles subtended at the center O of the circle.  The angles at the circumference also will be proved similarly.

angle AOB = angle BOC   as AB and BC are of same length.

angle AOD = 1/2 angle AOB : isosceles triangle and D is midpoint.

angle COE = 1/2 angle BOC : isosceles triangle  and E is midpoint.

Now the angle DOE = angle DOB + angle BOE = angle AOB  =  angle BOC.

================
2nd problem

AB is the common chord.  AC is the diameter of the 1st circle.  Then the angle ABC is the angle subtended by the diameter AC at the point B on the circumference. Thus it is 90 deg.

Similarly, in the 2nd circle, the diameter AD subtends angle ABD at the point on the circumference.  So it is 90 deg.

The sum of the angles ABC and ABD at point B is 180 deg.  So CBD is a straight line, the angle at B is equal to straightline angle.

http://brainly.in/question/77660
http://brainly.in/question/77656