YTC asked in 科學及數學數學 · 6 years ago

F.5 Maths geometry

question: http://postimg.org/image/sa4gxxyxz/

First, i join A1B1 and A2B2, find the length of A1B1 by Pyth.thm. Then prove that

triangle OA1B1 and OA2B2 are similar and use (corr. sides similar triangles).

But I cannot find OA2 as OA2 and A2B2(=√2 OA2) cancel each other during the

calculation.

How should I solve the question?

Please help,Thank you~~!

1 Answer

Rating
  • 土扁
    Lv 7
    6 years ago
    Favorite Answer

    36.(a) (i)

    Join OC2.

    OC2 = OA1 = 1 cm (same radii)

    A2C2 = OA2 (sides of square)

    OA2² + A­2C2² = OC2²(Pythagoras's theorem)

    OA2² + OA2² = (1cm)²

    4OA2² = 2 cm²

    OA2 = (√2)/2 cm

    Join OC3.

    OC3 = OA2 = (√2)/2 cm (same radii)

    A3C3 = OA3 (sides of square)

    OA3² + A­3C3² = OC3²(Pythagoras's theorem)

    OA3² + OA3² = [(√2)/2cm]²

    2OA3² = 1/2 cm²

    OA3 = 1/2 cm

    Join OC4.

    OC4 = OA3 = 1/2 cm (same radii)

    A4C4 = OA4 (sides of square)

    OA4² + A4C4² = OC4²(Pythagoras's theorem)

    OA4² + OA4² = (1/2cm)²

    2OA4² = 1/4 cm²

    OA4² = 2/16 cm²

    OA4 = (√2)/4 cm

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