Tangent Lines and Circle Angles

Lines that appear to be tangent are​ tangent.

        What is the value of​ x?

Mathematical Equivalence

ON

Answer explanation

radii drawn to the point of tangency for right angles.

x = 360 - 90 - 90 - 120

x = 60

In the figure,PA and PB are the tangents to a circle of center 'O'. ∠AOB= 120⁰ then ∠APB =

• 60⁰

• 30⁰

• 120⁰

• 75⁰

Line HK is tangent to circle C at point J.

Find each measure.

m∠KJM = ​ ​ (a)   _ , m∠MJN = ​ (b)   , m∠HJN = ​ (c)  

• 48

• 63

• 222

• 192

• 69

• 138

Assume that lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?

• 90

• 309

• 129

• 39

Line HK is tangent to circle C at point J. Find each measure. m∠KJM = ​ ​ (a)   _ , m∠MJN = ​ (b)   , m∠HJN = ​ (c)  

• 48

• 63

• 222

• 192

• 69

• 138

A tangent line intersecting with a radius always creates a ____________ angle

• right

• acute

• obtuse

• straight

Using the tangent lines, find the value of x.

• 60

• 120

• 30

• 300

Find the measure of <E.

• 7

• 8

• 44

In the diagram, PQ and QR are tangents to a circle at P and R respectively. Which of the following statements is correct?

Point O is the center of each circle. Assume the lines that appear to be tangent are tangent. What is the value of the variable?

• 26

• 57

• 66

• 114