Question

Line ET is tangent to circle A at T, and the measure of Arc TG is 50°. What is the measure of angle G E T?

A) 130
B) 90 This one is not right
C)65
D) 50
Which of the following is the equation of a circle with a radius of 2.5 and its center at (4, -3)?


A) ( x - 4 ) ^ 2 +( Y + 3 )^ 2 = 2.5 
B) ( x + 4 )^ 2 + ( Y - 3 ) ^ 2 = 2.5
C) ( x - 4 ) ^ 2 + ( Y + 3) ^ 2 =6.25
D) ( x -4 ) ^ 2 + ( Y - 3 ) ^ 2 = 6.25

Answer 1

the picture of the question N 1) in the attached figure

Part 1)
we know that
The measure of the external angle is the semi difference of the arcs that it covers
so
∠GET=(1/2)*[arc TN-arc TG]---> 0.5*[180-50]----> ∠ GET=65°

the answer part 1) is the option
C)65

Part 2)Which of the following is the equation of a circle with a radius of 2.5 and its center at (4, -3)?

we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
where (h,k) is the center and r is the radius
(h,k)-----> (4,-3)
r=2.5
so
(x-h)²+(y-k)²=r²-----> (x-4)²+(y+3)²=2.5²-----> (x-4)²+(y+3)²=6.25

the answer part 2) is the option
C) ( x - 4 ) ^ 2 + ( Y + 3) ^ 2 =6.25