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# 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

- 土扁Lv 76 years agoFavorite 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