Question
Download Solution PDFAB is the diameter of a circle with centre O. If P be point on the circle such that ∠AOP = 110°, then the measure of ∠OBP is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB is the diameter of a circle with centre O. If P be point on the circle such that ∠AOP = 110°
Formula used:
Sum of the angles of triangle = 180°
Calculations:
As from figure,
⇒ OA = OP = OB = radius
In ΔOPB
⇒ OP = OB
so, ΔOPB is an isosceles triangle
⇒ ∠OPB = ∠OBP = x
As, AB is an striaght line
⇒ ∠AOP + ∠POB = 180°
⇒ ∠POB = 180° - 110° = 70°
In ΔOPB,
⇒ ∠O + ∠P + ∠B = 180°
⇒ 70° + x + x = 180°
⇒ 2x = 180° - 70° = 110°
⇒ x = 55°
⇒ Hence, The measure of the ∠OBP is 55º
Last updated on Jul 7, 2025
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