Tangent Circles in the Ratio 2 : 1
نویسندگان
چکیده
In this article we consider the following old Japanese geometry problem (see Figure 1), whose statement in [1, p. 39] is missing the condition that two of the vertices are the opposite ends of a diameter. (The authors implicitly correct the omission in the proof they provide on page 118.) We denote by O(r) the circle with centre O, radius r. Problem [1, Example 3.2]. The squares ACBD and ABCD have a common vertex A, and the vertices C and B, C and B lie on the circle O(R) whose diameter is BC, A lying within the circle. The circle O1(r1) touches AB and AC and also internally touches O(R), and O2(r2) is the incircle of triangle ABC. Show that
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