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 a
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