Question
Download Solution PDFPA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that ∠APB = 100°, then ∠OAB is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
∠APB = 100°
O is the centre of the circle.
PA and PB are two tangents drawn from P outside the circle
Concept used:
A tangent to a circle forms a right angle with the circle's radius.
The Sum of all angles of a quadrilateral is 360°.
Calculation:
A tangent to a circle forms a right angle with the circle's radius
⇒ ∠OAP = ∠OBP = 90°
The Sum of all angles of a quadrilateral is 360°
⇒ ∠OAP + ∠OBP + ∠APB + ∠AOB = 360°
⇒ 90° + 90° + 100° + ∠AOB = 360°
⇒ ∠AOB = 360° - 280°
⇒ ∠AOB = 80°
In ΔAOB
⇒ ∠AOB + ∠OAB + ∠OBA = 180°
⇒ 80° + x + x = 180°
⇒ 2x = 100°
⇒ x = 50°
∴ The value of ∠OAB is 50°.
Last updated on May 28, 2025
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