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# Ch 6 Geometry

### Ch 6 Terms and Conjectures

Question | Answer |
---|---|

At what angle does a radius meet a tangent line at the point of tangency? | right angle, 90 degrees |

Compared to the slope of a tangent line, what is the slope of a radius or diameter that meets the tangent line at the point of tangency? | It is the perpendicular slope, and is the opposite reciprocal of the slope of the tangent line. |

What word describes 2 or more lines that are perpendicular to the same line? | parallel |

What word describes 2 segments that meet at a point outside of a circle and are tangent to the same circle? | congruent |

What word describes 2 central angles that are determined by 2 congruent chords in the same circle? | congruent |

If 2 arcs in the same circle are congruent, then what is known about the chords that intercept these arcs? | the chords are congruent |

What angle is made at the intersection of a chord and its bisector if the bisector intersects the center of the circle? | right angle, 90 degrees |

What is being done to a chord if it is intersected by a perpendicular line from the center of the circle? | bisected |

In a circle, what point is always determined by the intersection of the perpendicular bisectors of 2 chords? | center of the circle |

If the distance (shortest distance, perpendicular distance) from a chord of 7 cm to the center of the circle is 3 cm, then what is the distance from the same center to any chord of length 7 cm? | 3 cm |

What word describes two chords in the same circle that are equidistant from the center of that circle? | congruent |

When 2 chords in the same circle are congruent, what else is congruent? | intercepted arcs, determined central angles, and the distance (shortest distance, perpendicular distance) from each chord to the center |

What construction on a chord will pass through the center of a circle? | perpendicular bisector |

What is an inscribed angle in a circle half the measure of? | intercepted arc |

What describes the degree measure of a central angle and its intercepted arc? | congruent |

If the sides of a central angle intersect a circle at the same points as the sides of an inscribed angle measuring 20 degrees, then what is the measure of the central angle? | 40 degrees |

What two measures are twice the measure of an inscribed angle in a circle? | the measure of the intercepted arc, and the measure of the central angle that intercepts the same arc |

What describes 2 inscribed angles that intercept the same arc? | congruent |

For an inscribed angle in a circle, what else is the angle inscribed in if it measures 90 degrees? | semicircle |

If an angle is inscribed in a semicircle, then what is the measure of the inscribed angle? | 90 degrees |

What is known about a quadrilateral inscribed in a circle? | opposite angles are supplementary (add up to 180 degrees) |

What is the name for a quadrilateral inscribed in a circle? | cyclic quadrilateral |

What is the sum of the interior angles of a quadrilateral inscribed in a circle? | 360 degrees (like every other quadrilateral!) |

When a circle is intersected by 2 or more parallel lines, what describes the intercepted arcs between the parallel lines? | congruent |

What are 2 forms of the equation for the circumference of a circle? | C = (pi)*d OR C = 2*(pi)*r |

What is pi? | C/d (the ratio of the circumference to the diameter, or circumference divided by diameter) |

How do you find the length of an arc using the degree measure of the arc and the circumference of the circle? | divide the arc measure by 360, then multiple by the circumference |

How do you find the degree measure of an arc using the length of the arc and the circumference? | divide the length of the arc by the circumference, then multiply by 360 |

What ratio is equal to the length of an arc divided by the circumference? | the degree measure of the same arc divided by 360 degrees |

What is the distance between the centers of two circles that are externally tangent? | the sum of the radii of both circles |

What is the difference between a chord and a secant? | a chord is a segment with endpoints located on a circle, and a secant is a line that intersects a circle in two points and continues beyond those points |

What is another name for a parallelogram inscribed in a circle? | rectangle |

What is the measure of an angle formed by two intersecting chords? | half the sum of the measures of the two intercepted arcs |

What is the measure of an angle formed by two secants intersecting outside a circle? | half the difference of the measure of the larger intercepted arc and the measure of the small intercepted arc |

What is the measure of an angle formed by a secant and a tangent intersecting outside a circle? | half the difference of the measure of the larger intercepted arc and the smaller intercepted arc |

What is the measure of an angle formed by intersecting tangents to a circle? | 180 degrees minus the smaller intercepted arc measure |

What is the measure of an angle formed by the intersection of a tangent and chord at the point of tangency? | half the measure of the intercepted arc |

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ascensiongeometry