Find the measure of a.
A. 60
B. 57
C. 40
D. 80

Option (C)

Step-by-step explanation:

Since angle 'a' is the inscribed angle of the given triangle

Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.

x = 2a ⇒ a =

By the tangent-chord theorem,

"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"

= 40°

Therefore, a = = 40°

Option (C) will be the answer.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.