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 ?

29°

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°