Question

geometry help with tangent lines

Answer 1

Assume that lines that appear tangent are tangent. Point O is the center of the circle . find the value of x. Figures are not drawn to scale. M<o=145

Answer 2

325
35
290
72.5

I got 72.5

Answer 3

Ab is tangent to O. If AO =12 and Bc=25, what is AB?

35
37
50
47

Answer 4

AB is tangent to circle O at B. Find the length of the radius r for AB=8 and AO=11.7. round to the nearest 10th if necessary

13.7
3.7
8.5
14.2

Answer 5

Here are the answers:

Assume that lines that appear tangent are tangent. Point O is the center of the circle . find the value of x. Figures are not drawn to scale. M<o=145

x = 35
because every tangent makes a right angle (90 degrees) with the radius (line to O), the sum of angles in kite formed is 360 degrees
360 = x + 90+ 90 + 145
x = 180 - 145 = 35 degrees

Answer 6

Ab is tangent to O. If AO =12 and Bc=25, what is AB?

OA = OC = 12 both are the circle's radius, correct?
OB = OC + CB = 12 + 25 = 37
The angle formed by the tangent and the radius at the point A is a right angle, i.e. 90 degrees, so we can apply Pythagoras theorem as follows:
OB^2 = OA^2 + AB^2
37^2 = 12^2 + AB^2
1369 = 144 + AB^2
1369 - 144 = AB^2
1225 = AB^2
so AB = SQRT(1225) = 35

Answer 7

AB is tangent to circle O at B. Find the length of the radius r for AB=8 and AO=11.7. round to the nearest 10th if necessary

same as prev.one - use Pythagoras theorem because the triangle ABO is right-angled at the point B, so
AO^2 = OB^2 + AB^2
11.7 ^2 = r ^2 + 8 ^2
136.89 = r^2 + 64
136.89 - 64 = r^2
so r = SQRT(72.89) = 8.5