farngarloc (1 Viewer)

[farngarloc]

two circles intersect at A and B. The tangent to the first circle at A cuts the second circle and D and the tangent to the second circle at B cuts the first circle at C. Prove that AC and DB are parallel.

Thanks for the help!

 

[Mark576]

Produce AD to a point E, and join AB.
Then: ∠CAE = ∠ABC (angle between tangent and a chord through the point of intersection is equal to the angle in the alternate segment)
∠ABC = ∠ADB (similarly)
Hence ∠CAE = ∠ABC = ∠ADB
=> ∠CAE = ∠ADB
=> AC||DB (corresponding angles are equal)

 

[farngarloc]

Thanks for your help Mark

great!

 

[Mark576]

No problem :wave: