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If A, B, C and D are four points such th...

If A, B, C and D are four points such that `angleBAC=45^(@) and angleBDC=45^(@)`, then A, B, C and D are concyclic.

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To determine if points A, B, C, and D are concyclic given that ∠BAC = 45° and ∠BDC = 45°, we can follow these steps: ### Step 1: Understand the Given Angles We have two angles: - ∠BAC = 45° - ∠BDC = 45° ### Step 2: Identify the Segments Both angles are formed with respect to points B, A, C, and D. We need to analyze the segments in which these angles lie. ### Step 3: Recognize the Circle Property According to the properties of circles, if two angles are subtended by the same chord in the same segment of a circle, then those angles are equal. ### Step 4: Apply the Circle Theorem Since both angles ∠BAC and ∠BDC are equal (both are 45°), we can conclude that they are subtended by the same chord AC in the same segment of the circle. ### Step 5: Conclude the Cyclic Nature Since the angles are equal and subtended by the same chord, we can conclude that points A, B, C, and D lie on the same circle. Therefore, A, B, C, and D are concyclic. ### Final Conclusion Thus, the statement that A, B, C, and D are concyclic is true. ---
To determine if points A, B, C, and D are concyclic given that ∠BAC = 45° and ∠BDC = 45°, we can follow these steps: ### Step 1: Understand the Given Angles We have two angles: - ∠BAC = 45° - ∠BDC = 45° ### Step 2: Identify the Segments ...
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