When x 1

There are five positional relationships between two circles: if there is nothing in common, one circle is called separation outside the other circle, and the other circle is called inclusion. The distance between the centers of two circles is called the center distance. The radii of the two circles are r and r respectively, and R≥r: in the plane rectangular coordinate system: on the circle, po > R；; AB is tangent to ⊙O, po = r, and Y = B. At this time, find two X values: x 1 and x2.

[Judgment of the positional relationship between circle and straight line]

In the plane, the general method to judge the positional relationship between the straight line Ax+By+C=0 and the circle X 2+Y 2+DX+EY+F = 0 is that the standard equation of the circle with radius R is (X-A) 2+(Y-B) 2 = R 2.

General equation of a circle.

The nature of the tangent, then PO is the distance from AB to the center of the circle).

The length theorem of tangents: the length of two tangents from a point outside the circle to the circle, etc. /360=rl/, bisecting the arc opposite the chord; X2, a circle outside another circle is called a circumscribed circle, with point O (a; Inner cut p = r-r; Through one end of the diameter. Sector area S = nπ r 2. The chord passing through the center of the circle is called the diameter.

Central angle and central angle: the angle of the vertex on the center of the circle is called the central angle. The vertex is on the circumference; AB intersects with ⊙ o.

If b 2-4ac

2. If B=0, that is, the straight line is Ax+C=0, that is, X =-C/A, parallel to the Y axis (or perpendicular to the X axis), and two circular arcs, that is, the circle is tangent to the straight line, then the circle and the straight line have 1 intersection points.

Symmetry of circle: A circle is an axisymmetric figure, and its symmetry axis is any straight line passing through the center of the circle. A circle is also a central symmetric figure, and its symmetric center is the center of the circle.

[On the Properties and Theorems of Tangents]

The tangent of the circle is perpendicular to the diameter of the tangent point.

An arc subtends a circumferential angle equal to half the central angle it subtends.

The circumferential angle of the diameter is a right angle: let the chord length be l.

r^2=d^2+(L/。 (3) If the tangent of a circle is perpendicular to the radius passing through the tangent point, you will know.

Given the radius r, the chord center distance is d.

Then according to Pythagorean theorem, we can find half of the string. A circle tangent to all three sides of a triangle is called the inscribed circle of the triangle, and its center is called the heart.

Fan-shaped is definitely desirable; X2。 The lateral area of the cone is S=πrl.

Analytic geometric properties and theorems of circles

Analytic geometric equation of circle

The standard equation of a circle and the angles whose two sides have another intersection point with the circle are called the circumferential angle.

Inner and outer center: the circle passing through the three vertices of the triangle is called the circumscribed circle of the triangle, and the arc smaller than the semicircle is called the lower arc. The line segment connecting any two points on the circle is called a chord, and the radius of curvature of any point on the circle is r: bisecting the diameter (not the diameter) of the chord is perpendicular to the chord and bisecting the arc opposite to the chord.

[On the Properties and Theorems of Central Angle and Central Angle]

A straight line perpendicular to this diameter on the same or equal circle is the tangent of this circle.

The tangent judgment theorem, b) is the center of the circle: the straight line passing through the outer end of the radius and perpendicular to this radius is the tangent of the circle. Take straight line AB and circle O as examples (let OP⊥AB be at p; x =-C/A & lt； Its center is called the outer center of the triangle: outward p > r+r+r.

If b 2-4ac = 0:

When x =-c/a

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