Q2 of 33 Page 40

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.

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° )


More from this chapter

All 33 →
1

Suppose we draw circle with the bottom side of the triangles in the picture as diameter. Find out whether the top corner of each triangle is inside the circle, on the circle or outside the circle.

 3

If circles are drawn with each side of a triangle of sides 5 centimetres, 12 centimetres and 13 centimetres, as diameters, then with respect to each circle, where would be the third vertex?

 4

In the picture, a circle is drawn with a line as diameter and a smaller circle with half the line as diameter. Prove that any chord of the larger circle through the point where the circles meet is bisected by the small circle.

 5

Prove that the two circles drawn on the two equal sides of an isosceles triangle as diameters pass through the midpoint of the third side.