Question

AD, AC, DB, CB and AB are chords of a circle with center O.
∘∘
∠ABC=96 and∠ADB=45.Findthevalueof∠CAB.

Answer 1

$\huge\mathcal\pink{ANSWER:-}$

∠ADB = 105°  chord AC and BD intersect at P such that∠APB is equal to 120 and ∠PBC is equal to 15

$Step-by-step \: \: explanation:$

∠DBC = ∠PBC  (as P lies on BD)

=> ∠DBC = 15°

120° = ∠DAP + ∠ADP  ( Exterior angle of traingle = Sum of two opposite interior angles)

∠DAP = ∠DAC   as P lies on AC

∠ADP = ∠ADB   (as P lies on BD)

120° = ∠DAC + ∠ADB

∠DAC = ∠ DBC  ( angle subtended by same chord CD)

∠DAC = 15°

=> 120° =  15° + ∠ADB

=> ∠ADB = 105°

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