Circle Properties and Circle Theorems Diagnose

a) Choose from the options below by typing the correct letter to complete the sentence:

Radii and tangents which meet at the same point on the circumference of a circle…

A: are perpendicular

B: are of equal length

C: are parallel

D: always form an angle of 45 degrees

E: are of equal length and form a right angle

F: always form an angle of 30 degrees.

π + − ÷ × < > ≤ ≥ π

b) In the circle above on the left, which has centre O and angle AOB = 150°, angle ACB is π + − ÷ × < > ≤ ≥ π ° and angle ADB is π + − ÷ × < > ≤ ≥ π °.

c) Choose from the options below by typing the correct letter to complete the sentence:

In the circle on the right above, the alternate segment theorem tells us that…

A: angle CBD equals angle BAT

B: angle CAB equals angle CBD

C: angle BCA equals angle CBD

D: angle BDC equals angle CAB

E: angle BAT equals angle BCD

F: angle BAT equals angle ACB

π + − ÷ × < > ≤ ≥ π