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As shown in the figure, the diameter ab of ⊙ o is perpendicular to the chord CD at m, and M is the midpoint of radius ob, CD = 8cm
Connect OC,
∵ diameter ab ⊥ CD,
∴CM=DM=1
2CD=4cm，
∵ m is the midpoint of ob,
∴OM=1
2OB=1
2OC
According to the Pythagorean theorem, the following results are obtained
OC2=OM2+CM2
∴OC2=1
4OC2+42，
∴OC=8
Three
3cm
The length of diameter AB = 16
Three
3cm．
The diameter of circle O is ab = 16, M is the midpoint of ob, the chord CD passes through M, and the angle CMA = 30 is used to find CD
CD = numerator 16, root 3, denominator 3
As shown in the figure, the diameter ab of the center O is perpendicular to the chord CD, and the perpendicular foot P is the midpoint of ob As shown in the figure, the diameter ab of the circle center O is perpendicular to the chord CD, and the perpendicular foot P is the middle point of ob (OB is the radius), CD = 6cm, and the length of diameter AB is calculated. The grade is not enough to transmit the figure 0.0
If the radius of the circle is r, then OP = R / 2
According to the vertical diameter theorem, CP = CD / 2 = 3
According to Pythagorean theorem, OC ^ 2 = OP ^ 2 + CP ^ 2
So R ^ 2 = (R / 2) ^ 2 + 3 ^ 2
The solution is r = 2 √ 3
AB=2R=4√3
If the chord CD and diameter AB intersect at point P, the angle between them is 30 ° and the diameter is 1:5. If the two parts AB are equal to 6, then the chord CD is
AB=6
AP=1,AO=3
Po = 2, because the angle OPD is 30 degrees, the distance from O to CD is 1, and OD = 3
1^2+3^2=10
So CD = 2 root sign 10
As shown in the figure, AB is a chord of circle O, point C is the midpoint of arc AB, and CD is the diameter of circle O. the line L crossing point C intersects AB at point E, and circle O intersects point F
∵ point C is the midpoint of arc AB, CD is the diameter of circle o
As shown in the figure, the chord ab ⊥ CD of circle O is at point P, ab = CD = 8, the radius of circle O is 5, and find the length of Op
Make OE ⊥ CD at point E and of ⊥ AB at point F,
AB = CD = 8, CE = AF = 4
OC = OA = radius = 5, OE = of = 3
Ab ⊥ CD gets OE ⊥ of
OE is a square FP
Diagonal OP = 3 root sign 2
It is known that if the diameter of ⊙ o is 14cm, the chord AB = 10cm, the point P is the point above AB, and op = 5cm, then the length of AP is______ cm．
0
As shown in the figure, the diameter of circle O is 50, point P is the key point of chord AB, chord CD passes through point P, and ab = 40, CD = 48, try to find the value of cos ∠ APC
If the picture is not easy to paste, it should be explained whether there is one or two points in ABCD that are at both ends of the diameter of the semicircle in the figure
2. Connect the two points of op. because P is the midpoint of AB, Op bisects AB vertically, so OPB is a right triangle. The length of OP calculated by Pythagorean theorem should be 15
3. Add 1 and you need to add some conditions to solve the problem
As shown in the figure, AB is the diameter of ⊙ o, the chord CD is perpendicular to AB, P is any point on the arc CD (not coincident with points c and D) ∠ APC = ∠ APD? Why As shown in the figure, AB is the diameter of ⊙ o, the chord CD is perpendicular to AB, P is any point on the arc CD (not coincident with points c and D) ∠ APC = ∠ APD? Why
According to the Pythagorean theorem, the angle ACP = 90 degrees, AC = BC, so from Pythagorean theorem AP = 5, and from secant theorem, PD * PA = PC * Pb, PD = 4.2, and ad = 0.8, from angle ADB = 90 degrees, ab = 4 root sign 2, according to the Pythagorean theorem, DB = 5.6 and angle CDB is the circumference angle of the arc BC, so the angle CDB = 45 degrees, the angle BDF = 45 degrees, D
As shown in the figure, if the diameter of ⊙ o is 50, point P is the midpoint of chord AB, and chord CD passes through point P, and ab = 40, CD = 48, then cos angle APC = () process
Make the chord center distance of two strings (make the vertical segment of AB CD respectively from the center o) to obtain RT △, and then calculate the chord center distance
It can be known that cos ∠ APC = 7 / 15
RELATED INFORMATIONS
- 1. Given that AB is the diameter of ⊙ o, ab = 16, P is the midpoint of ob, the chord CD passes through the point P, ∠ APC = 30 °, then what is CD?
- 2. As shown in the figure, in the circle inscribed square ABCD with the side length of 1, P is the midpoint of the edge CD, and the straight line AP intersects the circle and the point e to find the length of the chord De
- 3. As shown in the figure, PA and Pb are two tangent lines of circle O, a and B are tangent points, AC is the diameter of circle O, ∠ BAC = 35 ° and the degree of ∠ P is calculated
- 4. If the length of a string is equal to the radius, then the radians of the central angle of the chord are? Why?
- 5. In a circle, if the chord AB = 1 / 3 of the root of 2 times and the chord center distance is 1, what is the radius of the circle? A, 2 B, 13 C, 11, D, 3 What to choose?
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- 7. Given that circle O1 and circle O2 are inscribed at point a, the chord ab of circle O1 intersects with circle O2 at point C, the ratio of radius of circle O1 to circle O2 is 2:3, ab = 12 emergency
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- 9. As shown in the figure, circle I is the inscribed circle of the triangle ABC, which is tangent to points D, e and F with AB, BC and Ca respectively, and the angle def = 50 degrees. Find the angle A
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- 13. In p-abcd of tetrahedral pyramid, ∠ ABC = ∠ ACD = 90 *, ∠ BAC = ∠ CAD = 60, PA ⊥ ABCD, PA = 2Ab, E.F. are PD, PC midpoint: CE is parallel to plane PA
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- 15. The ad of triangle ABC and CB is equal to c.ca CB.CE be equal to CD.AE Intersect BD with F, if the angle AEC is equal to 67 degrees
- 16. If the diameter ab of O intersects with the chord CD at point E, given AE = 6cm, EB = 2cm, ∠ CEA = 30 °, then the length of chord CD is () A. 8cm B. 4cm C. 2 Fifteen D. 2 Seventeen
- 17. As shown in the figure, AB and CD intersect at the point O, O is the midpoint of AB, ∠ a = ∠ B, is Δ AOC and Δ BOD congruent? Why?
- 18. As shown in the figure, AB and CD are the two chords of circle O. extending Ba and DC respectively, intersecting at points P, m, n are the midpoint of arc AB and arc CD, and Mn ⊥ Po Speed, please
- 19. As shown in Fig. 3, in the triangle ABC, ad bisects ∠ BAC, passing through B is vertical ad, perpendicular to foot is point E, crossing e is EF / / AC, and ab is intersected with F, AF and BF
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