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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.
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.
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