Q14 of 59 Page 83

In figure 3.92, O is the centre of a circle, chord PQ ≅ chord RS If∠ POR = 70°and (arc RS) = 80°, find -

(1) m(arc PR)


(2) m(arc QS)


(3) m(arc QSR)



(1) m(arc PR) = ∠POR = 70°


(2) ∠POQ + ∠ QOS + ∠ROS + ∠POR = 360°


As PQ = RS, ∠ POQ = ∠ROS = 80°


⇒ ∠POQ + ∠ QOS + ∠ROS + ∠POR = 360°


⇒ 80 + ∠QOS + 80 + ∠ 70 = 360


⇒ 230 + ∠ QOS = 360


⇒ ∠QOS = 130°


m(arc QS) = ∠QOS = 130°


(3) m(arc QSR) = ∠QOS + ∠ROS = 130 + 80 = 210°


More from this chapter

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12

Prove that any three points on a circle cannot be collinear.

 13

In figure 3.91, line PR touches the circle at point Q. Answer the following questions with the help of the figure.

(1) What is the sum of ∠ TAQ and∠ TSQ?


(2) Find the angles which are congruent to ∠ AQP.


(3) Which angles are congruent to ∠QTS ?


(4) ∠ TAS = 65°, find the measure of ∠TQS and arc TS.


(5) If ∠AQP = 42°and ∠SQR = 58° find measure of ∠ATS.



 15

In figure 3.93, m(arc WY) = 44°,m(arc ZX) = 68°, then

(1) Find the measure of ∠ ZTX.


(2) If WT = 4.8, TX = 8.0,YT = 6.4, find TZ.


(3) If WX = 25, YT = 8,YZ = 26, find WT.



 16

In figure 3.94,

(1) m(arc CE) = 54°,


m(arc BD) = 23°, find measure of ∠CAE.


(2) If AB = 4.2, BC = 5.4,


AE = 12.0, find AD


(3) If AB = 3.6, AC = 9.0,


AD = 5.4, find AE