Question

given: Two circles intersect each other at C and D. line AB is their common tangent. To prove: angle ACB + angle ADB=180˚

Answer 1

Answer:

Step-by-step explanation:

WE are given that 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.