1 .,兩架飛機沿著這條線相交.問題是在飛機上,在飛機;這些要點在于直線.構建等腰梯形(帶),圍成一個圓圈,可以刻頂點并躺在飛機和各一份
構建了.2、(三角形、高度和),平均從頂點.
如果一個三角形.構建,哪里是正中段和.證明解的存在,當且僅當
4 .考慮等腰triangle.讓半徑的圓的半徑,受到它的圓.證明之間的距離,這兩個圓圈中心
五.圓上有三種不同的分了.構裝體(僅使用一個直尺、羅盤)第一點,這樣可以在一圈的四邊形圖像.
6點和段.確定的軌跡,在空間的頂點直角一邊穿過,而另一方交叉段.
7 .一圈是在一個三角形.平行切線圓邊的三角是contructe.每一種切線triagnle隔斷.在每一種三角形,圍成一個圓圈是刻.發(fā)現的地區(qū)的所有4個刻有圈(在).
8.考慮與銳角.送進一分兩柱都被吸引到腳,其中,分別.交叉點上的高度.什么是位點被允許范圍內的對嗎
兩邊.
b)內部的.
九.我們是一個三角形,讓全取三分,將在其內部的兩側,這個三角形.證明面積至少三、三角形、小于或等于四分之一的地區(qū)的三角形.
選擇配方讓一個三角形,讓、3分,在部分,分別使用.證明了這一點
(拜托,加多點分嘛,打得很辛苦呢!）
英語翻譯
英語翻譯
1． Two planes,and ,intersect along the line .The point is given in the plane ,and the point in the plane ; neither of these points lies on the straight line .Construct an isosceles trapezoid (with ) in which a circle can be inscribed,and with vertices and lying in planes and respectively
2． Construct triangle ,given ,(the altitudes from and ),and ,the median from vertex .
3． Construct a triangle if ,and ,where is the midpoint of the segment and .Prove that a solution exists if and only if
4． Consider an isosceles triangle.let be the radius of its circumscribed circle and be the radius of its inscribed circle.Prove that the distance between the centers of these two circle is
5． On the circle there are given three distinct points .Construct (using only a straightedge and a compass) a fourth point on such that a circle can be inscribed in the quadrilateral thus obtained.
6． Point and segment are given.Determine the locus of points in space which are vertices of right angles with one side passing through ,and the other side intersecting segment .
7． A circle is inscribed in a triangle with sides .Tangents to the circle parallel to the sides of the triangle are contructe.Each of these tangents cuts off a triagnle from .In each of these triangles,a circle is inscribed.Find the sum of the areas of all four inscribed circles (in terms of ).
8． Consider with acute angle .Thorugh a point perpendiculars are drawn to and ,the feet of which are and respectively.The point of intersection of the altitudes of is .What is the locus of if is permitted to range over
a) the side ;
b) the interior of .
9． Let be a triangle,and let ,,be three points in the interiors of the sides ,,of this triangle.Prove that the area of at least one of the three triangles ,,is less than or equal to one quarter of the area of triangle .
Alternative formulation:Let be a triangle,and let ,,be three points on the segments ,,,respectively.Prove that
,
where the abbreviation denotes the (non-directed) area of an arbitrary triangle .
10． The parallelogram has ,and the triangle has all angles acute.Prove that circles radius and center cover the parallelogram if and only
1． Two planes,and ,intersect along the line .The point is given in the plane ,and the point in the plane ; neither of these points lies on the straight line .Construct an isosceles trapezoid (with ) in which a circle can be inscribed,and with vertices and lying in planes and respectively
2． Construct triangle ,given ,(the altitudes from and ),and ,the median from vertex .
3． Construct a triangle if ,and ,where is the midpoint of the segment and .Prove that a solution exists if and only if
4． Consider an isosceles triangle.let be the radius of its circumscribed circle and be the radius of its inscribed circle.Prove that the distance between the centers of these two circle is
5． On the circle there are given three distinct points .Construct (using only a straightedge and a compass) a fourth point on such that a circle can be inscribed in the quadrilateral thus obtained.
6． Point and segment are given.Determine the locus of points in space which are vertices of right angles with one side passing through ,and the other side intersecting segment .
7． A circle is inscribed in a triangle with sides .Tangents to the circle parallel to the sides of the triangle are contructe.Each of these tangents cuts off a triagnle from .In each of these triangles,a circle is inscribed.Find the sum of the areas of all four inscribed circles (in terms of ).
8． Consider with acute angle .Thorugh a point perpendiculars are drawn to and ,the feet of which are and respectively.The point of intersection of the altitudes of is .What is the locus of if is permitted to range over
a) the side ;
b) the interior of .
9． Let be a triangle,and let ,,be three points in the interiors of the sides ,,of this triangle.Prove that the area of at least one of the three triangles ,,is less than or equal to one quarter of the area of triangle .
Alternative formulation:Let be a triangle,and let ,,be three points on the segments ,,,respectively.Prove that
,
where the abbreviation denotes the (non-directed) area of an arbitrary triangle .
10． The parallelogram has ,and the triangle has all angles acute.Prove that circles radius and center cover the parallelogram if and only
英語人氣：117 ℃時間：2020-05-24 10:28:13
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