Monomath – CBSE | GSEB | IB | JEE Maths by Ajay Yadav (Math King of Katargam) – 15+ Years Experience. Study Notes, Video Lessons, Formula Sheets & PYQs.
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Circles

Previous Year Questions (2022-2024)

📅 Year 2022

  1. From point P, 10 cm from circle center O, tangent length PT = 8 cm. Find radius.
    Show Solution
    OT ⟂ PT (radius ⟂ tangent)\nOP2 = OT2 + PT2\n102 = r2 + 82 => r2 = 100 - 64 = 36\nr = 6 cm
  2. Prove that tangents drawn from external point to circle are equal.
    Show Solution
    Given: Circle O, external point P, tangents PA, PB at A,B.\nOA = OB (radii)\nOA ⟂ PA, OB ⟂ PB (radius ⟂ tangent)\nIn triangles OAP and OBP:\nOA = OB, OP = OP (common)\n∠OAP = ∠OBP = 90\n=> Triangles congruent (RHS)\n=> PA = PB

📅 Year 2023

  1. From point P, 10 cm from circle center O, tangent length PT = 8 cm. Find radius.
    Show Solution
    OT ⟂ PT (radius ⟂ tangent)\nOP2 = OT2 + PT2\n102 = r2 + 82 => r2 = 100 - 64 = 36\nr = 6 cm
  2. Prove that tangents drawn from external point to circle are equal.
    Show Solution
    Given: Circle O, external point P, tangents PA, PB at A,B.\nOA = OB (radii)\nOA ⟂ PA, OB ⟂ PB (radius ⟂ tangent)\nIn triangles OAP and OBP:\nOA = OB, OP = OP (common)\n∠OAP = ∠OBP = 90\n=> Triangles congruent (RHS)\n=> PA = PB

📅 Year 2024

  1. From point P, 10 cm from circle center O, tangent length PT = 8 cm. Find radius.
    Show Solution
    OT ⟂ PT (radius ⟂ tangent)\nOP2 = OT2 + PT2\n102 = r2 + 82 => r2 = 100 - 64 = 36\nr = 6 cm
  2. Prove that tangents drawn from external point to circle are equal.
    Show Solution
    Given: Circle O, external point P, tangents PA, PB at A,B.\nOA = OB (radii)\nOA ⟂ PA, OB ⟂ PB (radius ⟂ tangent)\nIn triangles OAP and OBP:\nOA = OB, OP = OP (common)\n∠OAP = ∠OBP = 90\n=> Triangles congruent (RHS)\n=> PA = PB