Question

two tangents are drawn to circle O from external point P. If the major arc formed has a measure of 280, find m

Answer 1

Which one do you think it is?

Answer 2

140 but im not sure at all

Answer 3

If the major arc is 280, then what is the minor arc?

Answer 4

Is it half the major arc?

Answer 5

no, the two arcs add to 360 degrees (since they make up a full circle)

Answer 6

so

major arc + minor arc = 360


and


minor arc = 360 - major arc

Answer 7

so the minor arc is 80 right?

Answer 8

yes

Answer 9

which would make m<p 80 since its a central angle?

Answer 10

so the central angle that subtends the tangent points is ?

Answer 11

no not quite

Answer 12

the central angle is 80, but m < P is not 80

Answer 13

hm im not sure...it cant be half of 80

Answer 14

if you draw a picture, you'll see that a quadrilateral forms


Two angles of this quadrilateral are 90 degrees (since they are the tangent points). So we have 90+90 = 180 degrees so far.


The remaining two angles MUST add to 180 degrees because all four angles in any quadrilateral add to 360 degrees.


So central angle + < P = 180

Answer 15

So < P = 180 - 80 = 100

Answer 16

so <p is 100?

Answer 17

exactly

Answer 18

thank you so much for actually explaining it to me!

Answer 19

you're welcome