In the semicircle with centre O, chords PQ = QR = RS . Find <QOR , < QPR , < PQR , and < QOS .
Answers
Answer:
hope it helps for solving
Given : In the semicircle with centre O, chords PQ = QR = RS.
To Find : angle QOR,
angle QPR,
angle PQR
angle QOS.
Solution:
PQ = QR = RS
=> ∠POQ = ∠QOR = ∠ROS
∠POQ + ∠QOR + ∠ROS = 180° straight line
=> ∠POQ = ∠QOR = ∠ROS = 60°
∠QOR = 60°
in ΔPOQ
PO = OQ = Radius and ∠POQ = 60°
=> ΔPOQ is equilateral triangle
=> ∠QPO = ∠PQO = 60°
Hence ΔPOQ , ΔQOR , ΔROS are equilateral triangle
∠PQR =∠PQO + ∠RQO = 60° + 60° = 120°
∠PQR = 120°
PQ = QR
=> ∠QPR = ∠QRP
∠PQR + ∠QPR + ∠QRP = 180°
120° + 2∠QPR = 180°
=> ∠QPR =30°
∠QOS = ∠QOR + ∠ROS
=> ∠QOS = 60° + 60° = 120°
=> ∠QOS = 120°
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