Telangana SCERT Solution Class IX (9) Math Chapter 12 Circles Exercise 12.2
(1) In the figure, if AB =CD and ∠AOB = 90o find ∠COD
Solution:
Given, AB = CD
∠AOB = 90o
AB & CD are two equal chords of the circle
∴ ∠COD = ∠AOB = 90o [∵angle subtended by two equal chords at the centre is equal]
(2.) In the figure, PQ = RS and ∠ΟRS = 48o . Find ∠OPQ and ∠ROS
Solution:
Given, PQ = RS
∠ORS= 48o
In △POQ & △ROS
(i) ∠ROS = ∠POQ [∵angle subtended by equal chords of a circle at the centre is equal]
(ii) RO = OP [radius of circle]
(iii) OS = OQ [radius of circle]
∴ △POQ ≅ △ROS by SAS
∴ ∠OPQ = ∠ORS = 48o [corresponding angles of congruent triangle are equal]
∠RSO = ∠PQO [corresponding angles of congruent △S are equal]
OR = OS [∵radius of circle]
∴In △ROS, △ORS = ∠OSR = 48o [opposite angles of equal sides are equal]
∴ ∠ORS + ∠OSR + ∠ROS = 180o [sum of angles of △ is 180o]
Or, 48 + 48 + ROS = 180o
Or, <ROS = 180o – 96o
Or, <ROS = 84o
(3) In the figure PR and QS are two diameters. Is PQ = RS?
Solution:
Given, PR and QS are two diameter of the circle
∴ O is the centre of circle since the intersection of two diameter of a circle is the centre.
∴ In △POQ & △ROS
(i) PO = OR [radius of circle]
(ii) OQ = SO [radius of circle]
(iii) ∠POQ = ∠ROS [vertically opposite angles]
∴ △POQ ≅ △ROS by SAS
∴PQ = RS [∵corresponding sides of congruent △S are equal]
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