find the unknown Angeles x and y
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kvnmurty:
is the intersection point at the middle the cener of circle? xy is not diameter.. is AB the diameter?
please tell
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x=50 deg. y=20 eg.
PQ is the tangent. Vertical line is xy , i think. so it is diameter.
∠xyP = 90 deg
Because xAyB is cyclic quadrilateral, ∠AyB = 180- 80 = 100°
∠ABy = 180°- x - 100° = 80°- x ---(1)
∠xAB = 180°- 80°-60° = 40°
Since diameter xy makes a 90° angle on the circle at A, ∠xAy = 90°
∠xAy = ∠xBy = 90°
So ∠ABy = 90°-60° = 30° ---(2)
From (1) and (2), we get x = 50°
∠xAB = ∠xyB = 40° angle made by the same chord xB.
∠ByQ = 50°
So ∠AyP = 180°- 100° - 50° = 30°
also ∠PAy = 180°-x = 130°
Hence, ∠y = 180°- 130° - 30° = 20°
PQ is the tangent. Vertical line is xy , i think. so it is diameter.
∠xyP = 90 deg
Because xAyB is cyclic quadrilateral, ∠AyB = 180- 80 = 100°
∠ABy = 180°- x - 100° = 80°- x ---(1)
∠xAB = 180°- 80°-60° = 40°
Since diameter xy makes a 90° angle on the circle at A, ∠xAy = 90°
∠xAy = ∠xBy = 90°
So ∠ABy = 90°-60° = 30° ---(2)
From (1) and (2), we get x = 50°
∠xAB = ∠xyB = 40° angle made by the same chord xB.
∠ByQ = 50°
So ∠AyP = 180°- 100° - 50° = 30°
also ∠PAy = 180°-x = 130°
Hence, ∠y = 180°- 130° - 30° = 20°
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