Circles

⭐ Important Questions

1. PQ and PR are tangents from P to circle with center O. Find ∠QOR if ∠QPR = 60°.
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   OQ ⟂ PQ, OR ⟂ PR (radius ⟂ tangent)\n∠OQP = ∠ORP = 90\nIn quadrilateral OQPR: ∠QOR + 90 + 60 + 90 = 360\n∠QOR = 120
2. In a circle of radius 5 cm, tangent at point P meets line through O at Q such that OQ = 13 cm. Find PQ.
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   OP ⟂ PQ\nPQ² = OQ² - OP² = 169 - 25 = 144\nPQ = 12 cm