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Find the area of the shaded region.

Mathematics

ScanSolve AI Answer

Step-by-step solution

2 steps
  1. Identify the given information and the shape.

    The figure shows a circle with center O and radius r=OA=OB=5r = OA = OB = 5 cm.
    TA and TB are tangents to the circle from an external point T.
    The distance from the center to the external point is OT=13OT = 13 cm.
    The angle ∠AOT=60∘\angle AOT = 60^\circ.
    The shaded area is the area of the quadrilateral OATB minus the area of the sector AOB.

  2. Check for consistency in the given information.

    In a circle, a tangent is perpendicular to the radius at the point of tangency. Therefore, ∠OAT=90∘\angle OAT = 90^\circ.
    Consider the right-angled triangle $\triangle O

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