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In the figure below PQR is a tangent to the circle at Q. TS is a diameter and TSR and QUV are straight lines. QS is parallel to TV. Angles SQR = 40° and TQV = 55°.
figure PQR tangent of the circle

  1. Find the following angles giving reasons each case.
    1. <QTS 
    2. <QRS 
    3. <QVT 
    4. <QUT 
  2. Given that QR = 8cm, and SR = 4cm. Find the radius of the circle. 

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  1.  
    1. <QTS = 40°
      Reason: Angles in the alternate segments are equal.
    2. <QRS = 10°
      Reason: Sum of angles in a triangle add up to 180°
    3. <QVT=35°
      Reason: Alternate angles in parallel lines are equal.
    4. <QUT = 50°
      Reason: <QST = 50°, subtended by chord TQ. TQ subtends <QUT, hence <QUT = 50°
  2. 8 × 8 = 4(4+x)
    16 + 4x =64
    4x = 48
    x = 12
    Radius = 12/2 = 6cm

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