In the given figure, AB is the diameter. The tangent at C meets AB produced at Q. If ∠CAB = 34°, Find:
(i)∠CBA (ii) ∠CQB
i) AB is diameter of circle. ∴ ACB = 90° In ΔABC, `∠`A + B + `∠`C = 180° ⇒ 34° + `∠`CBA + 90° = 180° ⇒ `∠`CBA = 56° ii) QC is tangent to the circle ∴ `∠`CAB = `∠`QCB Angle between tangent and chord = angle in alternate segment ∴ `∠`QCB = 34° ABQ is a straight line
Solution In the Given Figure, Ab is the Diameter. the Tangent at C Meets Ab Produced at Q. If ∠Cab = 34°, Find: (I)∠Cba (Ii) ∠Cqb Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.