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圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701012300106113873434020.jpg In the figure, PQR is an inscribed circle of triangle ABC. BC, AC and AB are tangents to the circle at P, Q and R respectively. It is given that angle ABC = 90 and the perimeter of ABC = 24a) it is given that BC =x, AB = x+d and AC =... 顯示更多 圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701012300106113873434020.jpg In the figure, PQR is an inscribed circle of triangle ABC. BC, AC and AB are tangents to the circle at P, Q and R respectively. It is given that angle ABC = 90 and the perimeter of ABC = 24 a) it is given that BC =x, AB = x+d and AC = x+2d i) find the value of d ii) find the radius of the circle b) find the length of AQ
最佳解答:
(a)(i) AC^2=AB^2+BC^2 (x+2d)^2=x^2+(x+d)^2 x^2+4xd+4d^2=2x^2+2xd+d^2 x^2-2xd-3d^2=0 (x-3d)(x+d)=0 x=3d or x=-d (rejected)Now BC+AB+AC=24 3d+4d+5d=24 d=2(ii) Let AR=a,BP=b,CP=c We know that a+b=8,b+c=6,a+c=10 Solve them a=6,b=2,c=4Let centre O, angle OBP=45 Since OP/BP=TAN OBP=1 =>radius of the circle = OP = BP =2(b) AQ=6 by the result of (a).
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CIRCLES MATH發問:
圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701012300106113873434020.jpg In the figure, PQR is an inscribed circle of triangle ABC. BC, AC and AB are tangents to the circle at P, Q and R respectively. It is given that angle ABC = 90 and the perimeter of ABC = 24a) it is given that BC =x, AB = x+d and AC =... 顯示更多 圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701012300106113873434020.jpg In the figure, PQR is an inscribed circle of triangle ABC. BC, AC and AB are tangents to the circle at P, Q and R respectively. It is given that angle ABC = 90 and the perimeter of ABC = 24 a) it is given that BC =x, AB = x+d and AC = x+2d i) find the value of d ii) find the radius of the circle b) find the length of AQ
最佳解答:
(a)(i) AC^2=AB^2+BC^2 (x+2d)^2=x^2+(x+d)^2 x^2+4xd+4d^2=2x^2+2xd+d^2 x^2-2xd-3d^2=0 (x-3d)(x+d)=0 x=3d or x=-d (rejected)Now BC+AB+AC=24 3d+4d+5d=24 d=2(ii) Let AR=a,BP=b,CP=c We know that a+b=8,b+c=6,a+c=10 Solve them a=6,b=2,c=4Let centre O, angle OBP=45 Since OP/BP=TAN OBP=1 =>radius of the circle = OP = BP =2(b) AQ=6 by the result of (a).
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