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 _______.

Answer 1

Answer:

65° at the center of the circle, then the angle

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 _______.

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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