For each diagonal of the quadrilateral shown, check whether the other two corners are inside, on or outside the circle with that diagonal as diameter.Circles

2)For each diagonal of the quadrilateral shown, check whether the other two corners are inside, on or outside the circle with that diagonal as diameter.

Ans

 

Case:1

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° )