Question

AP and BP are tangents to the circle with centre 0. If angle CBP = 25° and angle CAP =40 .Find


1) angle ADB

ii) angle AOB iii) angle ACB iv) angle APB

Answer 1

Given : AP and BP are tangents to the circle with centre O. ∠CBP = 25°  ∠CAP =40° .

To Find  : 1) ∠ADB  ii) ∠AOB iii) ∠ACB iv) ∠APB

Solution:

∠CBP = 25°

∠OBP  = 90°  ( tangent)

=> ∠CBO  = 65°

∠BCO = 65°   as OB = OC = Radius

=> ∠COB = 180° - 65° - 65° = 50°

∠CAP = 40°

∠OAP  = 90°  ( tangent)

=> ∠CAO  = 50°

∠ACO = 50°   as OA = OC = Radius

=> ∠COA = 180° -  50° - 50° = 80°

∠AOB = ∠COB +  ∠COA = 50° + 80° = 130°

∠AOB =   130°

∠ACB = ∠BCO +  ∠ACO = 65° + 50° = 115°

∠ACB =   115°

∠ADB = (1/2)∠AOB = (1/2)130° = 65°

∠ADB =   65°

∠AOB   + ∠APB  = 180°

=> 130° + ∠APB  = 180°

=> ∠APB  = 50°

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