(41) Intersection points between circles
11-30-2020, 02:19 PM
Post: #5
 Albert Chan Senior Member Posts: 2,230 Joined: Jul 2018
RE: Intersection points between circles We can also get x directly, from Law of Cosine.
Let R2 = angle corresponded to side r2 (the blue side)

$$r_2^2 = d^2 + r_1^2 - 2\;d\;r_1 \cos(R_2) = d^2 + r_1^2 - 2\;d\;x \\ ⇒ x = \large{d\over2} + {r_1^2 - r_2^2 \over 2d}$$

Let Δ = area of the triangle, vertices = (0,0), (x,h), (d,0)

$$Δ = \large{d\;h\over2}$$
$$⇒ h = \large{2Δ \over d}$$
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 Messages In This Thread (41) Intersection points between circles - rawi - 11-25-2020, 03:07 PM RE: Intersection points between circles - Albert Chan - 11-25-2020, 06:16 PM RE: Intersection points between circles - rawi - 11-25-2020, 06:48 PM RE: Intersection points between circles - Albert Chan - 11-26-2020, 12:22 AM RE: Intersection points between circles - Albert Chan - 11-30-2020 02:19 PM RE: Intersection points between circles - rawi - 11-30-2020, 05:19 PM RE: Intersection points between circles - Albert Chan - 11-30-2020, 09:03 PM RE: Intersection points between circles - Albert Chan - 12-01-2020, 12:17 AM RE: Intersection points between circles - SlideRule - 11-30-2020, 08:51 PM RE: Intersection points between circles - rawi - 12-01-2020, 09:25 AM RE: Intersection points between circles - Albert Chan - 12-01-2020, 11:59 AM RE: Intersection points between circles - rawi - 12-01-2020, 02:04 PM RE: Intersection points between circles - Albert Chan - 12-10-2020, 01:34 PM

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