CHAPTER 12: CIRCLES

CHAPTER 12: CIRCLES

1. LINES THAT INTERSECT CIRCLES

   • INTERIOR OF A CIRCLE: IS THE SET OF ALL POINTS INSIDE THE CIRCLE
   • EXTERIOR OF A CIRCLE: IS THE SET OF ALL POINTS OUTSIDE THE CIRCLE
   • CHORD: IS A SEGMENT WHOSE ENDPOINT LIE ON A CIRCLE
   • SECANT: IS A LINE THAT INTERSECTS A CIRCLE AT TWO POINTS
   • TANGENT: IS A LINE IN THE SAME PLANE AS A CIRCLE THAT INTERSECTS IT AT EXACTLY ONE POINT
     • POINT OF TANGENCY: THE POINT WHERE THE TANGENT AND A CIRCLE INTERSECTS
     • COMMON TANGENT: IS A LINE TANGENT TO TWO CIRCLES
   • CONGRUENT CIRCLES: IF AND ONLY IF THEY HAVE CONGRUENT RADDI
   • CONCENTRIC CIRCLES: ARE COPLANAR CIRCLES WITH THE SAME CENTER
   • TANGENT CIRCLES: TWO COPLANAR CIRCLES THAT INTERSECT AT EXACTLY ONE POINT

2. ARCHS AND CHORDS

   • CENTRAL ANGLE: VERTEX IS THE CENTER OF A CIRCLE
   • ARC: UNBROKEN PART OF A CIRCLE: CONSISTING OF TWO POINTS
   • MINOR ARC: POINTS ARE ON OR IN THE INTERIOR OF CENTRAL ANGLE
   • SEMICIRCLE: IF THE ENDPOINT OF AND ARC LIE ON A DIAMETER
   • ADJACENT ARCS: ARE ARCS OF THE SAME CIRCLE

3. SECTOR AREA AND ARC LENGTH

   • SECTOR OF A CIRCLE: IS A REGION BOUNDED BY TWO RADII OF THE CIRCLE AND THEIR INTERCEPTED ARC
   • SEGMENT: BOUNDED BY AN ARC AND IT'S CHORD
   • ARC LENGTH: DISTANCE ALONG AN ARCH

4. INSCRIBED ANGLES

   • INSCRIBED ANGLE: VERTEX IS ON A CIRCLE AND SIDES CONTAIN CHORDS OF THE CIR LE.
   • INTERCEPTED ARCH: ENDPOINTS THAT LIE ON THE SIDE OF AN INSCRIBED ANGLE
   • SUBTENDS: AN ANGLE IF ITS ENDPOINTS LIE ON THE SIDE OF THE ANGLE

5. ANGLE RELATIONSHIPS IN CIRCLES

   • THIS LESSON MOSTLY CONTAINS IMPORTANT THEOREMS THAT WE WOULD LIKE YOU TO KNOW, THERE ARE NOT SO MUCH DEFINITIONS

6. SEGMENT RELATIONSHIPS IN CIRCLES

   • SECANT SEGMENT: IS A SEGMENT OF A SECANT WITH AT LEAST ONE ENDPOINT ON THE CIRCLE
   • CENTRAL SECANT SEGMENT: IS A SECANT SEGMENT THAT LIES ON THE EXTERIOR OF THE CIRCLE WITH ONE ENDPOINT ON THE CIRCLE
   • TANGENT SEGMENT: IS A SEGMENT OF A TANGENT WITH ONE ENDPOINT ON THE CIRCLE

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