PQ is tangent at a point C to a circle with center 0 If AB is a diameteer and - Maths - Circles

Question

PQ is tangent at a point C to a circle with center 0 If AB is a
diameteer and angle CAB = 30 degree find angle PCA

Ishwarmani · Accepted Answer

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Given: PQ is a tangent
 AB is a diameter, ∠CAB=30°∠PCA=?In ∆AOC,As, AO=CO                   GivenSo, ∠CAO=∠OCA     Angles opposite to equal sides are equalor  ∠CAB=∠OCAbut  ∠CAB=30°So, ∠OCA=30°        
iSince, OC⊥PQ      Tangent is perpendicular to the radius at point of contact⇒∠PCO=90°⇒∠OCA+∠PCA=90°⇒30°+∠PCA=90°⇒∠PCA=90°-30°∴ ∠PCA=60°

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PQ is tangent at a point C to a circle with center 0. If AB is a diameteer and angle CAB = 30 degree find angle PCA