Q5 of 59 Page 73

Prove that, any rectangle is a cyclic quadrilateral.



In ABCD,


∠A = 90°{∵ angle of a rectangle is 90°.}


∠C = 90° {opposite angles are equals}


⇒∠ A + ∠ C = 180°


If opposite angles are supplementary, the quadrilateral is cyclic.


∴ ABCD is cyclic.


More from this chapter

All 59 →
3

is cyclic, ∠R = (5x - 13)°, ∠N = (4x + 4)°. Find measures of and

 4

In figure 3.58, seg RS is a diameter of the circle with centre O. Point T lies in the exterior of the circle. Prove that ∠ RTS is an acute angle.


 6

In figure 3.59, altitudes YZ and XT of

∆ WXY intersect at P. Prove that,



(1) WZPT is cyclic.


(2) Points X, Z, T, Y are concyclic.


 7

In figure 3.60, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠ NMS.