(41) Intersection points between circles

11262020, 12:22 AM
Post: #4




RE: Intersection points between circles
Another way is to solve for x, then get h (half chord length) XCAS> circle1 := x^2 + y^2  r1^2 = 0 XCAS> circle2 := (xd)^2 + y^2  r2^2 = 0 XCAS> chord := simplify(circle1  circle2); // equation for chord \((2d)x + (r_2^2  r_1^2  d^2)=0\\⇒ x = \large{d\over2} + {r_1^2  r_2^2 \over 2d}\) XCAS> p1, r1 := 13 + 4*i, 6.8 XCAS> p2, r2 := 6 + 10*i, 4.0 XCAS> d := abs(p1p2) → √85 ≈ 9.21954445729 XCAS> d1 := d/2 + (r1+r2)*(r1r2)/(2*d) → 6.24976648976 XCAS> h := sqrt((r1+d1)*(r1d1)) → 2.67963035203 Rotate/translate d1±h*i, back to intersection coordinates. XCAS> v1 := (p2p1)/d; → (7+6*i)/√85 = sign(p2p1) XCAS> p1 + v1*(d1+h*i) → 6.51094321226 + 6.03276708097*i XCAS> p1 + v1*(d1h*i) → 9.99870384656 + 10.1018211543*i 

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Messages In This Thread 
(41) Intersection points between circles  rawi  11252020, 03:07 PM
RE: Intersection points between circles  Albert Chan  11252020, 06:16 PM
RE: Intersection points between circles  rawi  11252020, 06:48 PM
RE: Intersection points between circles  Albert Chan  11262020 12:22 AM
RE: Intersection points between circles  Albert Chan  11302020, 02:19 PM
RE: Intersection points between circles  rawi  11302020, 05:19 PM
RE: Intersection points between circles  Albert Chan  11302020, 09:03 PM
RE: Intersection points between circles  Albert Chan  12012020, 12:17 AM
RE: Intersection points between circles  SlideRule  11302020, 08:51 PM
RE: Intersection points between circles  rawi  12012020, 09:25 AM
RE: Intersection points between circles  Albert Chan  12012020, 11:59 AM
RE: Intersection points between circles  rawi  12012020, 02:04 PM
RE: Intersection points between circles  Albert Chan  12102020, 01:34 PM

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