ABCD is a quadrilateral such that ∠ABC+∠ADC =180∘ inside the qua

1.	ABCD is a quadrilateral such that ∠ABC+∠ADC =180∘ inside the quadrilateral. Statement 1: the circumcircle of ΔABC intersects diagonal BD at D. Statement 2: the circumcircle of ΔABC intersects BD at D′inside the quadrilateral. Statement 3: the circumcircle of ΔABC intersects BD at D′ outside the quadrilateral. Statement 4: the circumcircle of ΔABC does not intersect BD at all. Statement 5: ABCD is called cyclic quadrilateral.
Answer» ABCD is a quadrilateral such that $∠$ ABC+ $∠$ ADC = $180^{\circ}$ inside the quadrilateral. Statement 1: the circumcircle of $Δ$ ABC intersects diagonal BD at D. Statement 2: the circumcircle of $Δ$ ABC intersects BD at $D^{^{'}}$ inside the quadrilateral. Statement 3: the circumcircle of $Δ$ ABC intersects BD at $D^{^{'}}$ outside the quadrilateral. Statement 4: the circumcircle of $Δ$ ABC does not intersect BD at all. Statement 5: ABCD is called cyclic quadrilateral.

ABCD is a quadrilateral such that ∠ABC+∠ADC =180∘ inside the quadrilateral. Statement 1: the circumcircle of ΔABC intersects diagonal BD at D. Statement 2: the circumcircle of ΔABC intersects BD at D′inside the quadrilateral. Statement 3: the circumcircle of ΔABC intersects BD at D′ outside the quadrilateral. Statement 4: the circumcircle of ΔABC does not intersect BD at all. Statement 5: ABCD is called cyclic quadrilateral.

Answer»

ABCD is a quadrilateral such that $∠$ ABC+ $∠$ ADC = $180^{\circ}$ inside the quadrilateral.

Statement 1: the circumcircle of $Δ$ ABC intersects diagonal BD at D.

Statement 2: the circumcircle of $Δ$ ABC intersects BD at $D^{^{'}}$ inside the quadrilateral.

Statement 3: the circumcircle of $Δ$ ABC intersects BD at $D^{^{'}}$ outside the quadrilateral.

Statement 4: the circumcircle of $Δ$ ABC does not intersect BD at all.

Statement 5: ABCD is called cyclic quadrilateral.