F.5 Maths geometry

YTC

2015-04-14 9:11 am

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~~!

回答 (1)

用戶26240

2015-04-14 9:53 am

✔ 最佳答案

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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