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In a circle with center O, RS is a diameter. RW is tangent to the circle at V. If SRV = 50^, find WRS?

Mathematics

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Here's a step-by-step solution for the geometry problem:

Given Information:

  • RS is a diameter of the circle with center O.
  • The line segment RW is tangent to the circle at point V.
  • R1^=∠SRV=50∘\hat{R_1} = \angle SRV = 50^\circ.

1.2.1 Calculate the size of WRS^\hat{WRS}

  1. Identify the angle in a semicircle.

    Since RS is a diameter, the angle subtended by the diameter at any point on the circumference is 90∘90^\circ. Therefore, ∠RVS=90∘\angle RVS = 90^\circ.

  2. Calculate $\angle RSV

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