Question

exam
question 1: standard g.c.4
when a tangent line and a radius intersect, they always form a ___ degrees angle.
a. 45
b. 180
c. 90
d. 360

question 2: standard g.c.4
a tangent line to a circle will touch the circle ___ times.
a. 3
b. 2
c. 0
d. 1

question 3: standard g.c.4
the 2 tangent theorem creates the special quadrilateral called a _____.
a. triangle
b. rhombus
c. square
d. kite

question 4: standard g.c.4
all of the angles in a kite add up to _____ degrees.
a. 360
b. 90
c. 180
d. 45

for questions 5 and 6 use the following diagram:
diagram of a circle with tangent lines and angles

Explanation:

Question 1

The tangent to a circle is perpendicular to the radius at the point of contact. Perpendicular lines form a 90 - degree angle. So the angle between a tangent and a radius is 90 degrees.

By the definition of a tangent to a circle, a tangent line touches the circle at exactly one point. A secant line intersects the circle at two points, but a tangent has only one point of contact.

The two - tangent theorem states that if two tangent segments are drawn from the same external point to a circle, then the lengths of the two tangent segments are equal. A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length. The two - tangent theorem creates a quadrilateral (formed by two tangents from an external point and the two radii at the points of contact) which is a kite because two pairs of adjacent sides (the tangent segments and the radii - but actually the tangent segments are equal and the radii are equal, and the angles between the tangents and radii are right angles, so the quadrilateral has two pairs of adjacent equal sides). A triangle is not a quadrilateral, a rhombus has all four sides equal, and a square is a special case of a rhombus. So the special quadrilateral is a kite.

Answer:

c. 90

Question 2