It is known that the equation of the circle is (x-3) ^ 2 + (y-4) ^ 2 = 25. If the straight line passing through the point (3,5) is cut by the circle, the length of the shortest chord is

It is known that the equation of the circle is (x-3) ^ 2 + (y-4) ^ 2 = 25. If the straight line passing through the point (3,5) is cut by the circle, the length of the shortest chord is

The shortest chord cut when the straight line passing through the point (3,5) is perpendicular to the diameter of the passing point
Distance from circle center to straight line d = √ [(3-3) ^ 2 + (5-4) ^ 2] = 1
Chord length Dmin = 2 √ (r2-d ^ 2) = 4 √ 6

The length of the string obtained by cutting the circle of a straight line Let a straight line be ax + by + C = 0, and the trajectory equation of a circle be (x-a) ^ 2 + (y-b) ^ 2 = C. if they intersect, what is the length of the truncated circle of the straight line? (formula) I want that formula... Forget the class. I can't find my notebook. It seems that there are three to deduce. Hungry... Send it if you can. Thank you~

There is a universal formula for the chord length cut by a straight line and a conic, [(x + X ') ^ 2-4xx'] * (1 + K ^ 2), where (x, y) and (x ', y') are the two intersections of the straight line and the conic, and K is the slope of the straight line. However, this formula is a derivation formula, and the derivation process must be written in the exam. Do you want to deduce the process?

Two strings intersect. One string is divided into two sections of 12cm and 18cm, and the other string is divided into 3:8. Find the length of the other string __

Set another chord length xcm;
Since the other string is divided into two segments of 3:8,
Therefore, the length of the two sections is 3
11xcm，8
11xcm，
The intersecting chord theorem can be obtained: 3
11x•8
11x=12•18
The solution is x = 33
So the answer is: 33cm

Calculation formula of arc length: l = n Π R / 180. What does L / N / Π / R / 180 / represent in geometry? What is a string?

N is the center angle, Π is 3.1415... R is the radius, 180 is the constant, and l is the arc length
A string is a line connecting any two points in a circle

Given the circle C: (x-1) 2 + y2 = 1, make any chord of the circle through the origin o, and find the trajectory equation of the midpoint of the chord

（1） Direct method: let OQ be any chord passing o, P (x, y) is the middle point, and the center C (1, 0)
Then CP ⊥ OQ, then
CP•
OQ＝0
‡ (x-1, y) (x, y) = 0, i.e. (x − 1)
2)2+y2＝1
4(0＜x≤1)
（2） Definition method: ∵∠ OPC = 90 °, the moving point P is in M (1
2, 0) is the center of the circle, OC is the diameter of the circle,
The trajectory equation of the point is (x − 1)
2)2+y2＝1
4(0＜x≤1)
（3） Parameter method: let the equation of moving string PQ be y = KX, which is determined by
y＝kx
(x−1)2+y2＝1
Get: (1 + K2) x2-2x = 0, let P (x1, Y1), q (X2, Y2),
If the midpoint of PQ is (x, y), then x = X1 + x2
2＝1
1+k2，y＝kx＝k
1+k2
Elimination of K (x − 1)
2)2+y2＝1
4(0＜x≤1)．

What is the formula for the distance from the origin to the chord length? d=?

The distance from the origin to the straight line ax + by + C is d = |c| / √ (a) ²+ B ²)