AD is the diameter of a circle with centre O and AB is a tangent to A. C is a point on the circle such that DC produced intersects the tangent at B and angle ABC=50°. Find angle AOC
Answers
Given : AD is the diameter of a circle with centre O and AB is a tangent to A. C is a point on the circle such that DC produced intersects the tangent at B and angle ABC=50°
To find : ∠AOC
Solution:
in Δ ABD
∠B = 50°
∠A = 90° ( as AB is tangent)
=> ∠D = 180° - 50° - 90°
=> ∠D = 40°
=> ∠ADC = 40°
∠AOC = 2∠ADC ( angle subtended by chord at center & arc egment)
=>∠AOC = = 2 * 40°
=> ∠AOC = 80°
or
OD = OC = Radius
=> ∠OCD = 40°
∠AOC = ∠OCD + ∠D
=> ∠AOC = 40° + 40°
=> ∠AOC = 80°
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