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Ch 6 Geometry

Ch 6 Terms and Conjectures

QuestionAnswer
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