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As shown in the figure, AB is the diameter of circle O, AB is perpendicular to chord CD at point P, and P is the midpoint of radius ob, CD = 6, then the diameter of circle O is
Cp * CP = AP * Pb (triangle APC is similar to triangle BPC) AP: Pb = 1:3
It can be concluded that Pb = root 3, so ob = 2PB = 2 times root 3
As shown in the figure, AB is the diameter of circle O, CD is the chord, ab ⊥ CD, the perpendicular foot is m, and M is the midpoint of ob, if AB = 12, find the length of CD
Connecting AC, BC
∵ AB is the diameter of circle o
∴∠ACB=90º
∵AB⊥CD
ν cm = DM [vertical diameter theorem]
∵ cam = ∠ BCM
∠AMC=∠CMB=90º
∴⊿AMC∽⊿CMB（AA‘）
∴AM/CM=CM/BM
This process is to prove the "projective theorem", if you want to know it, you can use it directly
∵ AB = 12, M is the midpoint of ob
∴OB=6,BM=3,AM=9
CM=√（AM×BM）=3√3
CD=2CM=6√3
AB is the diameter of ⊙ o, ab = 4, f is the midpoint of ob, and the chord CD ⊥ AB is in F, then CD=______ .
Draw a graph according to the meaning of the title, as shown in the figure: connect OC,
∵ diameter AB = 4, f is the midpoint of radius ob,
∴OC=OB=2，OF=1，
CD ⊥ AB,
/ / F is the midpoint of CD, i.e. CF = DF = 1
2CD，
In RT △ CFD, OC = 2, of = 1,
According to Pythagorean theorem: CF=
OC2−OF2=
3，
Then CD = 2cf = 2
3．
So the answer is: 2
Three
As shown in the figure, AB is the diameter of circle O, the intersection angle of chord CD and ab is ∠ APC = 30 °, BP = 1cm, AP = 5cm?
4√2cm
As shown in the figure, AB is the diameter of circle O, the chord CD and ab intersect at P, and ∠ APC = 45 ° if BP = 2, AP = 8, find the length of CD
Make OE ⊥ CD at point E
Then CE = De
∵BP=2,AP=8
∴OP=3
∵∠APC=45°
∴OE=3√2/2
If OC is connected, OC = 1 / 2Ab = 5
∴CE²=5²-(3√2/2)²
∴CD²=100-18=82
∴CD=√82
As shown in the figure, AB is the diameter of circle O, chord CD and ab intersect at P, and APC = 45. If BP = 2, AP = 8, find the length of CD As shown in the figure, AB is the diameter of circle O, the chord CD and ab intersect at P, and ∠ APC = 45 ° if BP = 2, AP = 8, find the length of CD
OE ⊥ CD is used to connect OC through the center o
∵AP＝8,BP＝2
∴AB＝AP+BP＝10
∴OC＝OB＝AB/2＝5
∴OP＝OB-BP＝5-2＝3
∵OE⊥CD,∠APC＝45
ν CE = de = CD / 2 (vertical diameter chord), OE = op / √ 2 = 3 / √ 2
∴CE＝√（OC²-OE²）＝√（25-9/2）＝√82/2
∴CD＝2CE＝√82
As shown in the figure, the diameter of ⊙ o is ab = 16, P is the midpoint of ob, and the ∠ APC formed by the intersection of chord CD and ab through point P is 30 ° and the length of CD is calculated
Make OE ⊥ CD at point E and connect OC
∵AB=16
∴OB=8
∵ P is the midpoint of ob
∴OP=4
∵∠APC=30°
∴OE=2
∵OC=8
According to Pythagorean theorem, CE = 2 √ 15 can be obtained
∴CD=2CE=4√15
If we know that the two chords AB, CD intersect with P in the circle O, and AP = 4, BP = 3, CD = 10, then CP =?
Because in circle O, two strings AB and CD intersect at point P, so AP × BP = CP × DP (intersecting chord theorem) because CP = 2, DP = 12, so AP × BP = 24, because AP △ BP = 2 △ 3, that is, AP = 2 / 3, so, 2 / 3 × (BP) ^ 2 = 24 (BP) ^ 2 = 36, so, BP = 6, so, AP = 4, so, ab = AP + BP means AB = 10
If we know that two chords AB, CD intersect with point P in circle O, and AP = 4, BP = 3, CD = 10, then CP =?
Because in circle O, two strings AB and CD intersect at point P, so AP × BP = CP × DP (intersecting chord theorem) because CP = 2, DP = 12, so AP × BP = 24, because AP △ BP = 2 △ 3, that is, AP = 2 / 3, so, 2 / 3 × (BP) ^ 2 = 24 (BP) ^ 2 = 36, so, BP = 6, so, AP = 4, so, ab = AP + BP means AB = 10
The two chords AB and CD of circle O are perpendicular to point P, AP = 4, BP = 6, CP = 3, DP = 8. Find the radius of circle o Sorry, there is no picture
Make om perpendicular to AB and m, on to CD and n
AB and CD are the two chords of circle O, ab = 10, CD = 11
According to the vertical diameter theorem
AM=MB=5,CN=ND=5.5
∵ AB, CD vertical
The ompn is easy to see as rectangular
PM = on = 5-4 = 1
If OC is connected, OC is the radius
OC^2=ON^2 +CN^2
It can be calculated by substitution
OC = (5 √ 5) / 2, radius is (5 √ 5) / 2
RELATED INFORMATIONS
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- 9. In circle O, the chords AB and CD intersect perpendicularly at the point E, AE = 5, CE = 1, be = 3. Find the radius of circle o
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