Q4 of 59 Page 73

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.



Given RS is the diameter


⇒ ∠ ROS = 180°


m(arc RS) = 180°


Now, ∠ RTS is an external angle.





Hence, ∠ RTS is an acute angle.


More from this chapter

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2

In figure 3.57, is cyclic. side PQ ≅ side RQ. ∠ PSR = 110°, Find-


(1) measure of ∠ PQR


(2) m(arc PQR)


(3) m(arc QR)


(4) measure of ∠ PRQ


3

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

 5

Prove that, any rectangle is a cyclic quadrilateral.

 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.