Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.
Since Δ ADF ≅ Δ DFC
∠ADF = ∠CDF
∴ ∠ADC = 2 ∠CDF
Similarly we can prove ∠CEB = 2∠CEF
Since || m
∠ADC + ∠CEB = 180^{o}
⇒2∠CDF + 2∠CEF = 180^{o}
⇒ ∠CDF + ∠CEF = 90^{o}
In Δ DFE
∠DFE = 90^{o}