Q2 of 23 Page 278

Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle. Also ∠A + ∠C = 180°, then prove that the vertex D also lie on the same circle.

In a quadrilateral, if the sum of opposite angles is 180°, then it is a


cyclic quadrilateral.


In quad. ABCD, A + C = 180°,


Therefore, ABCD is a cyclic quad.


In a cyclic quad., the vertices lie on the same circle. Thus, D also


lies on the same circle.


Hence, proved.


More from this chapter

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9

In the given figure ‘O’ is the centre of the circle and AB, CD are equal chords. If ∠AOB = 70°. Find the angles of the ∆OCD.

 1

Find the values of x and y in the figures given below.

i.


ii.


iii.

3

Prove that a cyclic rhombus is a square.

 4

For each of the following, draw a circle and inscribe the figure given. If a polygon of the given type can’t be inscribed, write not possible.

(a) Rectangle


(b) Trapezium


(c) Obtuse triangle


(d) Non-rectangular parallelogram


(e) Accute issosceles triangle


(f) A quadrilateral PQRS with as diameter.