Circle Geometry Question....Making me go crazy (1 Viewer)

[Schniz]

Two circles intersect in A and B and the 2 tangents at A are perpendicular. Are the two tangents at B also perpendicular? Give proof.

 

[word.]

given:
1. DCF is right angled.
2. D and F are circle centres. (normal of tangent to a circle passes circle centre)

rtp: DEF is right angled.

let E be the 2nd intersection pt between the circles.
construct DE & FE.

1. CF = EF (equal radii)
2. CD = ED (similarly)
3. DF is common.
thus CDF is cong. to DEF (SSS)

so DEF is right angled (corresp. angles in sim. tri.)

 

[Schniz]

thanks