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If point P is the point on the chord AB, connect OP, pass P as PC ⊥ OP, and PC intersect ⊙ o at point C. If AP = 4, Pb = 2, then the length of PC is () A. Two B. 2 C. 2 Two D. 3
Extend CP to ⊙ o at point D,
∵PC⊥OP，
∴PC=PD，
∵PC•PD=PB•PA，
∴PC2=PB•PA，
∵AP=4，PB=2，
∴PC2=8，
The length of PC is: 2
2．
Therefore, C
If AB is the diameter of circle O, the chord CD and ab intersect at point P and AP; Pb = 1; 5 OP = 2, angle DPB = 30 °, find the length of CD
∵OP=2,OA=OB,
AP：PB=1：5,
∴AP：OP=1：2,
ν radius OA = 3,
OQ ⊥ CD in Q,
∵∠DPB=30°,
∴OQ=1/2OP=1,
Connect OD,
∴DQ=∥(OD^2-OQ^2)=2√2,
∴CD=4√2.
As shown in the figure, AB is the diameter of circle O, the chord CS intersects with ab at point P, the angle AOD = 70 degrees, the angle APD = 60 degrees number
∵ AOD is the center angle corresponding to the circumference angle abd
∴∠ABD＝∠AOD/2＝70/2＝35
∵OB＝OD
∴∠BDO＝∠ABD＝35
∵∠AOD＝∠APD+∠CDO
∴∠CDO＝∠AOD-∠APD＝70-60＝10
∴∠BDC＝∠BDO-∠CDO＝35-10＝25°
As shown in the figure, AB is a chord of ⊙ o, OD ⊥ AB, perpendicular foot is C, intersect ⊙ o at point D and point E on ⊙ o (1) If ∠ AOD = 52 °, calculate the degree of ∠ DEB; (2) If OC = 3, OA = 5, find the length of ab
(1) ∵ AB is a string of ⊙ o, OD ⊥ ab,
Qi
AD=
DB，∴∠DEB=1
2∠AOD=1
2×52°=26°；
(2) ∵ AB is a string of ⊙ o, OD ⊥ ab,
/ / AC = BC, i.e. AB = 2Ac,
In RT △ AOC, AC=
OA2−OC2=
52−32=4，
Then AB = 2Ac = 8
As shown in the figure, AB is the diameter of ⊙ o, CD is the chord of ⊙ o, ∠ DCB = 30 °, then ∠ abd=______ .
∵∠DCB=30°，
∴∠A=30°，
∵ AB is ⊙ o diameter,
∴∠ADB=90°，
In RT △ abd,
∠ABD=90°-30°=60°．
So the answer is 60 degrees
In the circle O, the chords AB and CD intersect at P, and ab = CD. It is proved that Po bisects ∠ DPB
Make the vertical lines of AB and CD through O, and set the vertical feet as e and f respectively, then PE = PF, and OE = of, connect Po, then △ POF and △ Poe are congruent, then,,,,,,,, if the letters of each point are different, they may not be bisected
In the circle, CD is the chord, AB is the diameter, CD is perpendicular to AB, and the perpendicular foot is p.ab = 4? How to get CD? PA:PB = 1 :3 .. Less
∵PA:PB = 1 :3 ,AB=4
∴PA=1,OC=2
∴PO=1
And ∵ ab ⊥ PC
ν PC = √ 3 (Pythagorean theorem)
∴CD=2√3
∴PO=1,CD=2√3
As shown in the figure, chord CD in ⊙ o intersects with diameter AB at point E, M is a point on the extension line of AB, MD is the tangent of ⊙ o, D is the tangent point, if AE = 2, de = 4, CE = 3, DM = 4, then ob=______ ，MB=______ .
According to the intersecting string theorem, CE · ed = AE · EB {EB = CE · de
AE＝3×4
2=6．
∴OB=AB
2＝AE+EB
2＝2+6
2=4．
MD2 = MB · Ma = MB · (MB + BA)
Let MB = X
∴16=X•（X+8）⇒x=-4+4
2，x=-4-4
2 (shed)
So the answer is: 4, 4
2-4．
As shown in the figure, take the chord ab of circle O as the edge and make a square ABCD toward the outside of the circle Confirmation: 1. OC = ob If AB = 2, DM = 2 ^ 2, find the diameter of circle o
In this paper, we discuss the following problems: firstly, OA = ob, ad = BC, OBC = 90% ± oba = 90% ± OAB = open, OAB = open, so △ OAD ≌ △ OBC, OD = OC and on = OM, OMD = OMD ≌ △ OMD ≌ oncdm = cn2. Let og
As shown in the figure, the edge ab of the square ABCD with side length of 1 is the diameter of ⊙ o, CF cuts ⊙ o at point E, intersects ad at point F, and connects be (1) Calculate the area of △ CDF; (2) Find the length of segment be
(1) Let AF = x, then in RT △ FDC, (1-x) 2 + 1 = (x + 1) 2, ᙽ x = 14. s ⊙ FDC = 12 × CD × DF = 38. (2) connect OC to be at point G, connect OE.
RELATED INFORMATIONS
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