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As shown in the figure: in a circle with a diameter of 10 cm, the distance from the center of the circle to the chord AB is 4cm
Connect OA
∵ in the right angle △ OAE, OA = 1
2×10=5cm，OE=4cm．
∴AE=
OA2−OE2=
25−16=3．
∵OE⊥AB，
∴AB=2AE=2×3=6（cm）．
If the diameter of circle O is 10 cm and the chord center distance of chord AB is 3 cm, then the length of chord AB is
8 cm
According to the meaning of the title:
The radius of the circle is 5cm and the chord center distance is 3cm,
It's half a centimeter long: AB is easy to work out,
Then the string AB is 8 cm long
The chord AB divides the circle O into two parts: 1:2, ab = 8? My partner said the answer was four-thirds and root three But I can't figure it out
If the circle is divided into 1:2, the angle of the center of the circle to which the chord is directed is 120 degrees (because a circle is 360 degrees)
If the angle AOB is 120 degrees, AB is 8, and the end point of AB is p, then PA = Pb = 4, angle POB = 60 degrees, then chord center distance is 4 / root 3, so it is four thirds and root sign three
Just draw a picture~
If the radius of ⊙ o is 13, the chord ab ∥ CD, ab = 24, CD = 10, then the distance between AB and CD is () A. 7 B. 17 C. 7 or 17 D. 34
As shown in the figure, AE = 1
2AB=1
2×24=12，
CF=1
2CD=1
2×10=5，
OE=
AO2−AE2=
132−122=5，
OF=
OC2−CF2=
132−52=12，
① When the two chords are on the same side of the circle center, the distance = of-oe = 12-5 = 7;
② When the two chords are on the opposite side of the circle center, the distance = OE + of = 12 + 5 = 17
So the distance is 7 or 17
Therefore, C
The radius of the circle is 13, the chord AB is parallel to CD, the length of AB is 10, and the length of CD is 24. Find the distance between AB and CD
There are two situations
R = 13 distance d1 from center of circle to ab
d1=13²-5²=12
Distance d2 from center of circle to CD
d2=13²-12²=5
The distance between AB and CD is (D1 ± D2) = 17 or 7
In a circle with radius 13, chord AB is parallel to CD, and the distance between chord AB and CD is 7. If AB = 24, then the length of CD?
prove:
∵ as shown in the figure, the AB half OM of the chord with radius OA=13 is 12
The distance from the center of the circle O to the chord AB is OM= (13? -12?) =5
/ / AB / / CD parallel,
The distance from O to CD is on = 7-5 = 2
∴CD=2√（13²-2²）=2√165
Point P is a point in the equilateral triangle ABC, and PC = 3cm, Pb = 4cm, PA = 5cm
CPB = 150
As shown in the figure, a and B are two points on the same side of the straight line L, and the distances from a and B to L are 3cm and 5cm respectively, ab = 12cm. If point P is a point on L, then PA + Pb The minimum value of is
Make the symmetry point a ', connect a'B ∵ AP = a'p ? PA + Pb = a'p, pass through point a as BC ⊥ ad ∵ AB = 12, BD = 5-3 = 2 ᙽ ad = √ 140 ? a'c = ad = √ 140 ? a'B = √ [(√ 140) mm2 + 8 ∵ 204 ? the minimum value of PA + Pb is √ 204
As shown in the figure, there are three points a, B and C on the straight line L, and P is the point outside the line L. if PA = 5cm, Pb = 3cm, PC = 2cm, then point P is straight
Related knowledge:
Distance from point to line: make a vertical segment from point to line. The length of vertical segment is called the distance from point to line, and the vertical segment is the shortest
PA > Pb > PC
If PC is a vertical segment, the distance from P to L is 2 cm
If PC is oblique, the distance from P to L is less than 2 cm
So the distance between P and l is less than 2 cm
Given that the radius of circle O is 5cm, strings AB and CD are perpendicular to chord Mn, ab = 6cm, CD = 8cm, then the distance between AB and CD is_____ . This is a problem in our mathematics "vertical and string diameter",
1 cm or 7 cm
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