2022 · Q69
A circle is inscribed in a triangle ABC. It touches the sides BC, CA, AB at D, E, F respectively. What is ∠EDF equal to?
Elementary MathematicsCircles
- A90° - A
- B90° - (B+C)/2
- C90° - 2A
- D90° - ≤ft(A/2)
Explanation
Let I be the incentre: ∠EAF = A with ∠AEI = ∠AFI = 90°, so ∠EIF = 180°−A. Since D lies on the incircle, the inscribed angle EDF subtending arc EF is half the central angle EIF, i.e. 90°−A/2. The keyed option is D.