Question

Two circles intersect each
other at C and D. Line AB is their
cornmon angent.
To prove : angleACB +angleADB =180 degree​

Answer 1

GIVEN : The two circles intersect each other at C and D and the line AB is the common tangent, then

Angle made by the chord and tangent= angle in alternate segment,

therefore ∠CBA=∠CDB and ∠CAB=∠CDA.

Now, as ∠CDB+∠CDA=∠CBA+∠CAB

⇒∠ADB=180°-∠ACB ( because from the figure it is given that ∠CDB+∠CDA=∠ADB)

⇒∠ADB+∠ACB=180°

Hence proved.