maths question ? (1 Viewer)

[super.muppy]

The diagram shows two circles intersecting at A and B. The diameter of one circle is AC. On your diagram draw a straight line through A, parallel to CB, to meet the second circle in
D.

someone please Prove that BD is a diameter of the second circle.
&
Suppose that BD is parallel to CA. Prove that the circles have equal radii.


thankssss !

 

[Ayatollah]

because its parralel to AC, which is the diametre of the other circle
and if they both have the same diamter, they have the same radii

 

[super.muppy]

u cant say its parallel to AC can u ?

 

[Ayatollah]

yes u can..

draw two circles intersecting, then Make 'A' the upper point of intersection
all the lines should join up in the parallelgram ACBD (making A the top point, then going clockwise)

 

[Drongoski]

Why is this posted here ?

i) since AC is diameter of one circle, angle ABC = 90 deg (angle in a semi-circle)

But angle BAD = angle ABC (alternate angles, CB//AD)

.: angle BAD = 90 deg

.: BD must be a diameter of the other circle (angle in semi-circle = 90 deg)


ii) if BD//CA, then ACBD is a quadrilateral with 2 pairs of // sides

.: it is a //gram

.: diameter CA = diameter BD

i.e. the 2 circles have same radii