Circle (DSE Maths) @ vbd391t的部落格

標題:

Circle (DSE Maths)

發問:

O is the centre of the circle. AOB is the diameter of the circle, and it intersects the chord CD at M. If CM= 8 cm, MD= 6cm and OM=MA, find the radius of the circle.

最佳解答:

The answer is as follows : 圖片參考：https://s.yimg.com/lo/api/res/1.2/0b.2s4YFYSC26ktM5OVVhQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/https://farm4.staticflickr.com/3869/14955791576_1eab0048b4_o.png https://farm4.staticflickr.com/3869/14955791576_1eab0048b4_o.png 2014-08-22 03:03:03 補充： If you do not know intersecting chords, use the following 2 paragraphs to replace the 2nd paragraph. Join AD and BC. ∠AMD = ∠CMB (vert. opp. ∠s) ∠BAD = ∠DCB (∠s in same segment) ∠DAB = ∠BCD (∠s in same segment) ΔAMD ~ ΔCMB (AAA) AM / CM = MD / MB (r/2) / 8 = 6 / (3r/2) 3r2/4 = 48 r2 = 64 r = 8

其他解答:

Let OC=OD=r (radii) ∠MCO=∠MDO=θ (base ∠s,isos△) Using cos law, MC2+OC2-2(MC)(OC)cos∠MCO=OM2 82+r2-16rcosθ=r2/4 ... 1 MD2+OD2-2(MC)(OD)cos∠MDO=OM2 62+r2-12rcosθ=r2/4 ... 2 Combine 1&2, 82+r2-16rcosθ=62+r2-12rcosθ cosθ=7/r ... 3 Sub 3 into 1 82+r2-16r(7/r)=r2/4 3r2/4=48 r=8|||||pingshek 答得好好！ ╭∧---∧╮ │ .??? │ ╰/) ? (\\╯ 同學如果不明白 Intersecting chord 的話，可以考慮 △MAD ~ △MCB