Cyclic Quadrilateral

Geometry Level 2

The above figure shows a quadrilateral inscribed in a circle. Which of the following is always true?

∠ A D B = ∠ B C A \angle ADB=\angle BCA ∠ A C B = ∠ C B A \angle ACB=\angle CBA ∠ D A B = ∠ B C D \angle DAB=\angle BCD ∠ D B C = ∠ B D C \angle DBC=\angle BDC

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1 solution

From the figure, the intercepted arc of ∠ A D B \angle ADB and ∠ B C A \angle BCA is the same. Therefore, the inscribed angles are equal and will be always equal.

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