YTC 發問於 科學及數學數學 · 5 年 前

F.5 Maths circle

Picture: http://postimg.org/image/ifmvlghyr/

In the figure, X and Y are the centres of two equal circles. AR touches the circle at P and Q. AR passes through X and touches the circle with centre Y at D. If the two circles touch each other at S. Find θ.

A. 18.4°

B. 26.6°

C. 30°

D. It cannot be determined.

My finding: http://postimg.org/image/62a1ejsab/

I cannot find the actual value of θ. Is the answer is D or any things I have missed

so that the answer should be A,B or C?

Please help. Thank you!

更新:

RE 邊位都好 :

Why XYQP is rectangle?

2 個解答

評分
  • 5 年 前
    最佳解答

    XYQP is a rectangle, let XP be r, so XY is 2r.Triangle DXY is a right-angled triangle with right angle XDY.

    As DY is also having the length r, so,sin θ=DY/XY=r/2r=1/2therefore, θ=30° ⋯⋯ (C)

    2015-01-17 00:29:46 補充:

    They are two equal circles, and AR touch these two circles at P, Q.

    So, XP丄AR and YQ丄AR, that is, XYQP is a rectangle.

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  • You can draw XY and DY only

    It may be the easiest way to find θ by using sin θ

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