What Is the measure of minor Ark. DF given that line DE and line FE are tangent to o0
2 answers:
Answer:
Option B is correct.
Step-by-step explanation:
Given:
Circle with center O.
line DE and line FE are tangents to the circle.
∠DEF = 84°
To find: measure of minor arc that ∠DOF.
Construction: Join DO and FO.
We know that Tangents are perpendicular to the radius at point of contact.
⇒ ∠EDO = ∠EFO = 90°
Now, In Quadrilateral ODEF
∠DEF + ∠EDO + ∠FDO + ∠DOF = 360° ( Angle Sum Property of Quadrilateral )
84° + 90° + 90° + ∠DOF = 360°
∠DOF = 360 - 264
∠DOF = 96°
Therefore, Option B is correct.
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