ract asked in 科學及數學數學 · 1 decade ago

f4math 難題(quickly)

PA and QC are tangents.show that PQ=PA

http://images.u-state.com/i0304/1204641471.bmp

1 Answer

Rating
  • 1 decade ago
    Favorite Answer

    Pls. check if the question needs the proof to be PQ = QA instead of PQ = PA.

    Join AC and let ∠ABC = θ. Then ∠BCA = 90 (Angle in semi-circle)

    ∠QAC = ∠QCA = θ (Angle in alternate segment)

    So QA= QC since QCA is an isos. triangle.

    ∠PCQ = 180 - ∠BCA - ∠QCA = 90 - θ

    Also ∠CPQ = 180 - ∠BAP - ∠PBA = 90 - θ as ∠BAP = 90 for the reason of diameter perpendicular to tangent.

    So with ∠CPQ = ∠PCQ, CPQ is an isos. triangle with PQ = CQ

    Finally, PQ = CQ = QA

    Source(s): My Maths knowledge
    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.