As shown in the figure, the radius of ⊙ o is 1cm, and the lengths of strings AB and CD are respectively 2 cm, 1 cm, then the acute angle α between the strings AC and BD=______ Degree

As shown in the figure, the radius of ⊙ o is 1cm, and the lengths of strings AB and CD are respectively 2 cm, 1 cm, then the acute angle α between the strings AC and BD=______ Degree

Connect OA, ob, OC, OD,
∵OA=OB=OC=OD=1，AB=
2，CD=1，
∴OA2+OB2=AB2，
△ AOB is an isosceles right triangle,
Delta cod is an equilateral triangle,
∴∠OAB=∠OBA=45°，∠ODC=∠OCD=60°，
∵∠CDB=∠CAB，∠ODB=∠OBD，
∴α=180°-∠CAB-∠OBA-∠OBD=180°-∠OBA-（∠CDB+∠ODB）=180°-45°-60°=75°．

As shown in the figure, AB is the chord of chord circle O, Pb tangent circle O at point B, and op ⊥ OA intersects AB at point C. It is proved that Pb = PC

Where is the picture, please?

4. As shown in the figure: if chord BC passes through the midpoint P of radius OA of circle O and Pb = 3, PC = 4, then the diameter of circle O is () A.7 B.8 C.9 D.10

B,R/2*3R/2=3*4,R=4 ,D=8.

PA.PB Circle O at two points a and B, and pass through the intersection point m of AB and op to make string CD verification: PC / cm = od / OM Come on. It's urgent

∵ PA, Pb cut ⊙ o at points a and B, OP and ab intersect at point M
∴OA⊥PA,AM⊥OP
∴△OAM∽△OPA
∴OM/OA=OA/OP
∵OA=OC=R
∴OM/OC=OC/OP
∵∠MOC=∠COP
∴△OCM∽△OPC
∴∠MCO=∠CPO
∵OD=OC=R
∴∠MCO=∠CDO
∴∠CPO=∠CDO
∴△CPM∽△ODM
∴PC/CM=OD/OM

As shown in the figure, the straight line PAB intersects circle O at point a, B, PC tangent circle O at point C. If Po = 13, PC = 12, the distance from the center O to the chord AB is 3, find the length of PA

R=OC=√(13^2-12^2)=5
Go to point D in ab
AD=√(5^2-3^2)=4
PD=√(13^2-3^2)=4√10
therefore
PA = 4 √ 10 + 3 or PA = 4 √ 10-3

Point P is a point in ⊙ o with radius of 5, and op = 3cm. Among all chords passing through point P, the number of chords with integer length is () A. 1 B. 2 C. 3 D. 4

As shown in the figure,
Make ab ⊥ op on P,
AP=BP，
In RT △ AOP, Op = 3, OA = 5,
AP=
52−32＝4，
∴AB=8，
Therefore, the length of chord passing through point P is between 8 and 10, and there are 2 strings with chord 9,
Of all the chords passing through point P, there are 8, 9, 10,
A circle is an axisymmetric figure,
The number of chords with integer length passing through point P is 4
Therefore, D

If OP = 8, how many chords with integer length in the chord passing through point P? Please attach a picture

There are 16
Through calculation, the shortest chord is 12 and the longest chord is 20. There are 9 integers between 12 and 20
According to the symmetry change, there are 9 * 2 = 18 integer chords. Because the shortest chord and diameter are repeated once, the result is 18-2 = 16

Given that the radius of circle O is 13, P is a point in circle O, Op = 5, then how many strings of integer length can be made through point P (main process)

If the length of chord passing through point P is an integer, its length can be 26 [one], 25 [two], 24 [one]

There is a point P in the circle whose center is O and radius is 15. If OP = 12, how many chords with integer length passing through point P? Do the numbers 18 and 30 count? More specifically, how many? 12 or 14?

The string perpendicular to op should be the shortest one
The shortest chord through P is 9 * 2 = 18, which is obtained by Pythagorean law
The longest chord passing through point P is 30 in diameter
So all integers from 18 to 30 are
Of course, these two strings exist. The diameter is a special string. It should be 13

Given that point P is a certain point in ⊙ o with radius of 5, and op = 4, among all chords passing through point P, the chord with integer length has______ Article

As shown in the figure, AB is the diameter, OA = 5, Op = 4, passing through point P as CD ⊥ AB, intersecting with points c and D
According to the vertical diameter theorem, point P is the midpoint of CD;
From Pythagorean theorem, PC=
OC2−OP2=
If 52 − 42 = 3, CD = 2pc = 6, then
CD is the shortest chord passing through point P, and its length is 6;
AB is the longest string through P, which is 10
Therefore, the chord length of the chord passing through point P can be 2 of 7, 8 and 9, and there are 8 strings of integer length in total
So the answer is: 8