Question

question 5: standard g.c.4
both angle cba and cda are equal to 90 degrees because ...
a. tangent radius theorem
b. triangle postulates
c. definition of a quadrilateral
d. two tangent theorem
question 6: standard g.c.4
the measure of angle bcd = ?
a. 180
b. 90
c. 58
d. 42
question 7: standard g.c.2 i
arc length is different from arc measure because ...
a. measure is a length (cm) and length is an angle (degrees)
b. measure is an angle (degrees) and length is a distance (cm)
c. they are equal when both inside a circle
d. the measure can be calculated using algebra and length using geometry
question 8: standard g.c.2 i
if a circle has a central angle of 20 degrees and a radius of 2, what is the arc length?
a. 1.2
b. 0.69
c. 4.2
d. 0.005
question 9: standard g.c.2 i
arc length is a fraction of the ____ which is represented by 2πr.
a. radius
b. circumference
c. area
d. volume
question 10: standard g.c.2 i
sector area is a fraction of the ____ which is represented by πr².
a. radius
b. circumference
c. area
d. volume

Explanation:

Question 5

The tangent - radius theorem states that a tangent to a circle is perpendicular to the radius at the point of tangency. So if CB and CD are tangents and BA and DA are radii (or vice - versa), then angles CBA and CDA (where the tangent meets the radius) would be 90 degrees. Triangle postulates are about triangle congruence or similarity, not about tangent - radius perpendicularity. The definition of a quadrilateral is a four - sided figure, which has nothing to do with these angles being 90 degrees. The two - tangent theorem is about the lengths of two tangents from a common external point, not about the angle between tangent and radius.

Assuming this is a cyclic quadrilateral or related to a circle with right angles at CBA and CDA. If we consider the properties of circles and quadrilaterals, and if we know that the sum of opposite angles in a cyclic quadrilateral is 180, but if we have other information (maybe from a diagram not fully shown, but common in such problems), if angle BAD is, say, 122 degrees (since 180 - 58 = 122, and using cyclic quadrilateral or tangent - secant angle properties), then angle BCD would be 58 degrees. 180 is a straight angle, 90 is a right angle, 42 doesn't fit the common angle relationships here.

Arc measure is the measure of the central angle in degrees (or radians) that subtends the arc. Arc length is the actual distance along the arc, measured in units like centimeters. Option a has them reversed. Option c is wrong because they are not equal (unless the circle has a radius of 1 and in radians, but generally not). Option d is wrong as both arc measure and length can be calculated using geometric concepts (arc measure with central angle, arc length with formula \(s = r\theta\) where \(\theta\) is in radians).

Answer:

a. Tangent radius theorem

Question 6