Math 10_Q2: Theorems on tangent, secants and angles

Quiz by Rey Alferez Fernandez

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- Q1
What is the measure of an exterior angle formed by two intersecting secants?

Equal to the sum of the intercepted arcs

Equal to half the difference of the intercepted arcs

Equal to the half of the sum of the intercepted arcs

Equal to the difference of the intercepted arcs

45s - Q2
In the tangent-point-secant theorem, what is the relationship between the radius and the tangent at the point of tangency?

The radius is perpendicular to the tangent.

The radius and tangent are parallel.

The tangent is equal in length to the radius.

The tangent bisects the radius.

30s - Q3
If a secant and a tangent line intersect on a circle, what is the relationship between the exterior angle and the intercepted arc?

There is no specific relationship between them.

The exterior angle is half the intercepted arcs.

The exterior angle is is twice the intercepted arc.

They are equal

30s - Q4
What is the tangent-point-secant theorem used for?

Calculating the circumference of a circle

Finding the area of a circle.

Determining the length of a tangent line

Analyzing the relationship between secants and tangents

30s - Q5
If two secants intersect inside a circle, what can you say about the angles formed?

They are complementary.

They are congruent.

They are supplementary.

Their measures are half the sum of the intercepted arcs.

30s - Q6
In the tangent-point-secant theorem, what does the term "point of tangency" refer to?

The point where the tangent touches the circle.

The point where two secants intersect.

The center of the circle.

The midpoint of the tangent.

30s - Q7
What is the purpose of the tangent line in the tangent-point-secant theorem?

To bisect the secant.

To intersect the secant at a specific point.

To create an exterior angle with the secant.

To create a right angle with the secant.

30s - Q8
If two secants intersect outside a circle, what is the relationship between the exterior angle and the intercepted arc?

They are equal.

There is no specific relationship between them.

The exterior angle is twice the intercepted arc.

The exterior angle is half the intercepted arc.

30s - Q9
Which theorem is applied when calculating the measure of an inscribed angle formed by two chords inside a circle?

Intersecting Secants Theorem

Tangent-Point-Secant Theorem

Exterior Angle Theorem

Inscribed Angle Theorem

30s - Q10
If a tangent line is drawn to a circle, what can be said about the angle between the tangent and the radius at the point of tangency?

It is always acute.

It is always right.

It can be any type of angle.

It is always obtuse.

30s - Q11
What is the measure of an inscribed angle when it intercepts a semicircle?

90 degrees

45 degrees

180 degrees

360 degrees

30s - Q12
What theorem that states

*the measure of an angle inscribed in a circle is one-half the measure of the central angle.?*Intersecting Secant Theorem

Tangent Theorem

Perpendicular Bisector of a Chord Theorem

Inscribe Angle Theorem

30s - Q13
In the given illustration, what is the measure of angle 1, if the measures of the two intercepted arcs are 88 and 42 degrees respectively?

65 degrees

42 degrees

130 degrees

88 degrees

30s - Q14
In the figure below, what is the value of x?

100

^{ 0}60

^{ 0}160

^{ 0}50

^{ 0}30s - Q15
If an inscribed angle in a circle has a measure of 60 degrees, what is the measure of its intercepted arc?

30 degrees

60 degrees

120 degrees

180 degrees

30s