PQR and XYR are two secants of a circle which cut at point R outside the circle. PY is the diameter of the circle. If ∠PRX = 32°, ∠QPY = 38° then find the value of ∠QYR.?

38°
70°
52°
58°

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 4 : 58°

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In the figure, PY is the diameter of the circle

⇒ ∠PXY = 90° (Angle made by diameter on the circumference)

⇒ ∠QXY = ∠QPY = 38° (Angles made by same chord QY)

⇒ ∠PXQ = 90 – ∠QXY = 90 – 38 = 52°

⇒ ∠PYQ = ∠PXQ = 52° (Angles made by same chord PQ)

⇒ ∠PYR + ∠YPR + ∠YRP = 180

⇒ ∠QYR = 180 – ∠PYQ – ∠YPR – ∠PRY

∴ ∠QYR = 180 – 52 – 38 – 32 = 58°

4 views Answered 2022-09-04 04:29

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