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प्रश्न
In the given figure, AC is a tangent to circle at point B. ∆EFD is an equilateral triangle and ∠CBD = 40°. Find:
- ∠BFD
- ∠FBD
- ∠ABF
उत्तर
Given - In Diagram, ∆FED is an equilateral triangle, ∠CBD = 40°
To Find -
- ∠BFD,
- ∠FBD,
- ∠ABF
(a) ∠BFD = ∠CBD = 40° ....[Alternate segment theorem]
(b) ∠FBD is opposite to ∠FED.
So, It is a cyclic Quadrilateral. So, ∠FBD and ∠FED will be Supplementary to each other.
∴ ∠FBD + ∠FED = 180° ....[Cyclic Quadrilateral]
∠FBD + 60° = 180°
∠FBD = 180° - 60°
∠FBD = 120°
(c) AC is a line segment.
So, ∠ABF = 180° - (120° + 40°) ....[Line Segment]
∠ABF = 180° - 100°
∠ABF = 20°
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