In a triangle DEF, O is the center of the incircle ABC. ∠DEF = 60°

1.	In a triangle DEF, O is the center of the incircle ABC. ∠DEF = 60°, ∠DFE = 75°. Find ∠AOB(a) 75° (b) 45° (c) 135° (d) cannot be determined.
Answer» Answer : (c) 135º In ∆ DEF, ∠ EDF = 180° – (60° + 75°) = 180° – 135° = 45° ∠OAD = ∠OBD = 90° (Tangents DE and DF are perpendicular to radii OA and OB respectively at A and B) ∴ In quad . DAOB, ∠AOB = 360° – (90° + 90° + 45°) = 360° – 225° = 135°.

In a triangle DEF, O is the center of the incircle ABC. ∠DEF = 60°, ∠DFE = 75°. Find ∠AOB(a) 75° (b) 45° (c) 135° (d) cannot be determined.

Answer»

Answer : (c) 135º

In ∆ DEF, ∠ EDF = 180° – (60° + 75°)

= 180° – 135° = 45°

∠OAD = ∠OBD = 90° (Tangents DE and DF are perpendicular to radii OA and OB respectively at A and B)

∴ In quad . DAOB, ∠AOB = 360° – (90° + 90° + 45°)

= 360° – 225° = 135°.

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In a triangle DEF, O is the center of the incircle ABC. ∠DEF = 60°, ∠DFE = 75°. Find ∠AOB(a) 75° (b) 45° (c) 135° (d) cannot be determined.

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