Question
Download Solution PDFAB is the diameter of a circle with centre O. P be a point on it. If ∠AOP = 95°, then ∠OBP __________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
AB is a diameter of circle centre O,
Formula used :
Linear pair angle, angle on straight line = 180°
Calculation
∠AOP = 95 °
∠POB = ( 180 ° - 95 °) = 85°
∆ POB = ∠P = ∠B ( Isosceles triangle )
⇒ ∠POB = 85°
∆ POB = ∠POB + ∠ OBP + ∠ BPO = 180°
⇒ 180° = 85°+ 2 × ∠OBP
⇒ 95/2 = ∠OBP
⇒ 47.5° = ∠OBP
The value of ∠OBP is 47.5°.
Shortcut Trick∠OBP = 1/2 × of ∠AOP
∠OBP = 1/2 × of 95 = 47.5
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