I have 2 scalene triangle (with 1 side common) inscribed in a circle.
Triangle 1: One side has length = 10 and other x
Triangle 2: One side has length = 12 and other x
I need to find the length of the common side x. Here's how it looks:
Any hint or a formula I can use?
2026-04-04 04:20:57.1775276457
Length of a common side of 2 inscribed triangles
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Hint: Join all other chords and by angles in the same segment, you'll see the two adjacent chords are equal (i.e. the two adjacent sides at the bottom of the cyclic quadrilateral). Now equating the equal sides by cosine law:
$$10^2+x^2-2(10)x\cos 30^{\circ}=12^2+x^2-2(12)x\cos 30^{\circ}$$
Can you proceed?