Question

PQ and RS are two parallel chords of a circle such that PQ = RS = 12 cm and PQ
subtends 65° at the center of the circle, then the angle subtended by RS at the center
is _______.
a) 180°
b) 130°
c) 65°
d) 32.5°

Answer 1

Answer:

65 degree is the answer because equal chord substend equal angle at center

Answer 2

Given : PQ and RS are two parallel chords of a circle such that PQ = RS = 12 cm

PQ subtends 65° at the center of the circle,

To Find : the angle subtended by RS at the center is _______.

a) 180°

b) 130°

c) 65°

d) 32.5°

Solution:

Angle subtended by congruent chord/arc of a circle at center are congruent

PQ = RS = 12 cm

Hence Chord PQ ≅  chord RS

as Chord PQ ≅  chord RS

=> ∠POQ ≅ ∠ROS  where O is center of circle

=> m ∠POQ =  m∠ROS

m ∠POQ =  65°

=> m∠ROS  =  65°

the angle subtended by RS at the center is 65°

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