AB is common tangent to two circles that intersect at C & D. AD is
tangent to smaller circle & BD is tangent to larger circle Find angle ADB
Answers
∠ADB = 180° - ∠ACB.
To find : Angle ADB, ∠ADB = ?
Given :
- AB is a common tangent to two circles.
- They intersect at C and D.
- AD is tangent to smaller circle.
- BD is tangent to larger circle.
To find the angle ADB :
From the figure,
∠ACB + ∠ADB = 180°
∠CBA = ∠CDB -----> ( 1 )
∠CAB = ∠CDA ------> ( 2 )
Add the equation ( 1 ) and ( 2 ), we get
∠CDB + ∠CDA = ∠CBA + ∠CAB -----> ( a )
∠CBA + ∠CAB + ∠ACB = 180°
∠CBA + ∠CAB = 180° - ∠ACB -----> ( b )
Substituting the equation ( 1 ) and ( 2 ) values in the equation ( a ) and ( b ), we get
∠CDB + ∠CDA = 180° - ∠ACB -----> ( c )
∠CDB + ∠CDA = ∠ADB -----> ( d )
Subtracting the equation ( c ) and ( d ), we get
0 = 180° - ∠ACB - ∠ADB.
∠ADB = 180° - ∠ACB
Therefore, the ∠ADB = 180° - ∠ACB .
To learn more...
1. Two circles intersects eah other at C and D.line AB is common tangent how to prove angle ABC+angleADB=180degree. give full solution fast
brainly.in/question/6804169
2. Two equal circles with centres o and o' touch each other at x. oo' produced meets the circle with centre o' at a. ac is tangent to the circle with centre o, at the point c. o'd is perpendicular to ac. find the value of do'/co
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