Question

Circle question

I found y = 16, but I absolutely do not know how to find x.

Answer 1

is A the center of the circle?

Answer 2

yes

Answer 3

Segment PS is the diameter since point A lies on the segment.

So central angle PAS is 180 degrees.


So m < arc PT + m < arc TS = 180 degrees


which tells us that the inscribed angles TPS and TSP add up to half that...180/2 = 90 degrees.

So this means that


m < TPS + m < TSP = 90


6x+11 + 9x+19 = 90


15x+30 = 90


15x = 90-30


15x = 60


x = 60/15


x = 4

Answer 4

ok then 6x+11 + 9x + 19 = 90
because angle PTS is 90 degrees (angle subtended on circle by a diameter)

Answer 5

which gives x = 4 as Jim said

Answer 6

Thank you both! sadly I cannot give medals to both of you. But how did you find out that arc PT and TS are 90 degrees?

Answer 7

What if it's 100 degrees and 80 degrees? How do you know they're both equal?

Answer 8

The inscribed angles (not the arcs) add to 90 degrees. So they aren't 90 degrees each.