Q2 of 23 Page 266

In the figure, PQ = RS and ∠ORS = 48°. Find ∠OPQ and ∠ROS.

In ORS,


∠ORS = ∠OSR (radius of circle)


∠OSR = ∠ORS = 480


∠OSR + ∠ORS + ∠ROS = 180


⇒ 48 + 48 + ∠ROS = 180


⇒ 96 + ∠ROS = 180


⇒ ∠ROS = 180-96


⇒ ∠ROS = 180-96


⇒ ∠ROS = 84


We know “Angles subtended by equal chords at the center of a circle are equal”.


∠POQ = ∠ROS = 840


In POQ,


∠POQ + ∠OPQ + ∠OQP = 180


840 + x + x = 180


840 + 2x = 180


2x = 180-84


2x = 96


x =


x = 48


∠OPQ = 48


More from this chapter

All 23 →
2

State true or false.

i. A circle divides the plane on which it lies into three parts. ( )


ii. The area enclosed by a chord and the minor arc is minor segment. ( )


iii. The area enclosed by a chord and the major arc is major segment. ( )


iv. A diameter divides the circle into two unequal parts. ( )


v. A sector is the area enclosed by two radii and a chord ( )


vi. The longest of all chords of a circle is called a diameter. ( )


vii. The mid point of any diameter of a circle is the centre. ( )

 1

In the figure, if AB = CD and ∠AOB = 90° find ∠COD

 3

In the figure PR and QS are two diameters. Is PQ = RS?

 1

Draw the following triangles and construct circumcircles for them.

(i) In ∆ ABC, AB = 6cm, BC = 7cm and ∠A = 60°


(iii) In ∆ XYZ, XY = 4.8cm, ∠X = 60° and ∠Y = 70°


(iii) In ∆ XYZ, XY = 4.8cm, ∠X = 60° and ∠Y = 70°