Question

If A, B, C and D are four points such that $\angle BAC={45}^{\circ }and\angle BDC={45}^{\circ }$ then A, B, C, D are concyclic

Answer 1

In geometry, a set of points are said to be concyclic if they lie on a common circle.

Given $\angle BAC={45}^o$ and $\angle BDC={45}^o$

From the figure, it can be seen that they are lying on the circumference of the circle by same chord $BC$.

But from the theorem we also know that, the angle subtended by the chord at the circle are equal .

Here angles are equal , which means that these $4$ points are concyclic .

$\therefore$ $A,B,C,D$ are concyclic.