b Notice that AD and CD are tangent to the central circle and they intersect each other in the exterior of it.
A
a m∠ACE = 100
B
b m∠ADC = 20
Practice makes perfect
a Let's begin by taking a close look at the given diagram.
Notice that AC is secant to the central circle and CE is tangent. Additionally, they intersect each other at the tangency point C. Thus, the measure of ∠ACE equals one half the measure of the intercepted arc — in this case, ABC.
We are told that m ABC= 200. Let's substitute it into the formula above to find the required angle.
m ∠ACE = 1/2( 200) = 100
b We notice that AD and DE are tangent to the central circle of the soccer field at A and C respectively.
Then, the measure of ∠ADC is equal to one half the measure of the difference of the intercepted arcs – namely, ABC and AC.
By using the measure of the major arc we will find the measure of the minor arc.
m ABC_(200) + m AC = 360 [-0.15cm]
⇓
m AC = 160
Finally, let's substitute the measures of both arcs to find the measure of the required angle.
