AB is a tangent at the point D on a circle with centre O. EF is a diameter, which when produced meets the tangent AB at A. If ∠EAB = 32°, then what will be the measure of ∠FDA ?
Answer & explanation
Correct answer: option 4
OD is perpendicular to AB, so ∠ODA = 90°
Let ∠FDA = θ
Now ∠OFD = 32° + θ (exterior angle)
⇒ ∠OFD = ∠ODF = 32° + θ
We know, ∠ODA = 90°
∠ODA = ∠FDA + ∠ODF
∠ODA = 32° + θ + θ
90° = 32° + 2θ ⇒ \(\frac{58°}{2}\) = θ
∠FDA = θ = 29°