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圆内接四边形 ABCD 内,∠A = 90°,AB = a,BC = b,其面积为 c²,求CD,DA 及圆半径之长.
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证从平行四边形之一顶点作线至对边之中点,三等分四边形之对角线.
如图,已知正方形ABCD的边CD上任意一点E.延长BC到F,使CF=CD.设BE与DF相交于G,求证:BG⊥DF.
已知ABCD,A'B'C'D'都是正方形(如图),而A'、B'、C'、D'分别把AB、BC、CD、DA分为m:n,设AB=1.(1)求A'B'C'D'的面积;(2)求证A'B'C'D'的面积不小于1/2.
联四边对边中点之两直线,必互为二等分,试证之.
于四边形之内,取一点不在两对角线之交点之上者,试证明从此点至各顶点之距离之和大于两对角线之和.
ABCD is a rectangle. and a straight line APQ cuts BC in P & DC extended in Q. Locate the point P so that the sum of the areas of the two triangles ABP&CPO may be a minimum.
PQRS为平面四边形,QR=1,∠PQR= ∠QRS= 70°,∠PQS=15°,∠PRS= 40°.若∠RPS=θ.PQ=α,PS=β,则4αβsinθ属于下列哪个区间【 】
试作一正方形,与一已知长方形之面积相等.
求作一四角形,与一已知四角形等角而外切于一定圆.
设ABCD为一平行四边形,AC为对角线,由B作任意直线各交AC、CD及AD于F、G及E,求证EF·FG=BF².
设两弦于圆内相交,其两线分之积,彼此相等,试证明之.
圆内各等弦中点之轨迹为一同心圆周,试证之.
设由圆外一点作一切线一割线,证明此切线为割线及其圆外线分的比例中率.
设一圆之半径为 25 尺,其外切四边形之圆界为 400 尺,试求此四边形之面积。
作通过二定点,中心在一定直线上之圆.
任意之外切四边形,相对两边之和等于其他相对两边之和,试证明之.
If two circles tangent at C and a common exterior tangent touches the circles in A and B, the angle ACB is a right angle.
两圆相外切 (tangent externally) 于 A,又有一外公切线 (common external tangent) 切两圆于 B 及 C,试证 ∠BAC 为直角(right angle).
已知三角形之三角及其面积,求作其圆.
试证圆内之等弦距圆心均等.又证圆内之两等弦相交割其所割相当之部分各相等.
Homologous sides of two similar polygons have the ratio of 5 to 9 , the sum of the areas is 212 sq. ft. Find the area of each figure.
Twos tations,A and B on opposite side of a mountain, are both visible from a third station C. The distance AC=3m.CB=5m and the angle ACB=60°. Find the distance between A and B.
Two straight roads intersect at an angle of 30°. If two automobiles start at the same time at the junction, one at the rate of 60 miles an hour and the other atthe rate of 40 miles an hour, how far apart will they be in 15 minutes?
一定点 D在 AB 及 AC 两直线间,求作过 D至 AB、AC 两线之直线,并 D为所作线之三等分点之一点,并证有二此等线.
试言已知三角形之两角及一角之对边,求作其形之方法.
n 多边形诸角之和=______.
何谓圆:___________________________.
过一已知点,作直线分已知等腰梯形为两等积形.
作直线垂直于一已知线,与已知圆相切.
如图,在三角形ABC中∠BAC=60°,BD平分∠ABC,交AC于D,CE平分∠ACB交AB于E,BD和CE交于F,则∠EFB=【 】