Answer :

Now we have been given a quadrilateral ABCD:

__Case 1 :__ let us now draw a diagonal BD in quadrilateral ABCD

● Draw a circle considering, BD as a diagonal.

● As ∠A and ∠C are larger then 90° . Thus, point A and C lies inside the circle.

(As seen above, point on a circle, such an angle is a right angle.

Point outside the circle , such an angle is larger than 90°

Point inside the circle, such an angle is smaller than 90° )

__Case 2:__ let us now draw a diagonal AC in quadrilateral ABCD

Also, By angle sum property of quadrilateral

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 105° + ∠B + 110° + 55° = 360°

⇒ ∠B + 270° = 360°

⇒ ∠B = 360° – 270° = 90°

● Draw a circle considering, AC as a diagonal.

● As ∠B is 90° . Thus, point B lies on the circle.

As ∠D is smaller then 90°. Thus, point D lies outside the circle.

(As seen above, point on a circle, such an angle is a right angle.

Point outside the circle , such an angle is larger than 90°

Point inside the circle, such an angle is smaller than 90° )

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