Can anyone help me solve this circle? ​

Explanation:

Focus on triangle OCT. We can see that the triangle is isosceles because OT = OC are two radii of the same circle. That consequently means angles T and C are the congruent base angles (rotate the triangle to see what I mean). The base angles are opposite the congruent sides.

Since base angle C is 35 degrees, that makes base angle T this measure as well.

We just found angle CTO is 35 degrees. Angle PTO is supplementary to this, so it is 180-35 = 145 degrees.

Now focus solely on quadrilateral PTOQ. The goal is to find angle O, aka angle QOT. We found angle T in the paragraph above and it's 145 degrees. Angle Q is 90 degrees assuming segment PR is tangent to the circle at point Q.

Recall that for any quadrilateral, the interior angles always add to 360

let x be the measure of angle O, aka angle QOT

P+T+O+Q = 360

60+145+x+90 = 360

x+295 = 360

x = 360-295

x = 65

Therefore, angle QOT is 65 degrees

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.