ghettorapnelsop10kus
25.05.2021 •
Mathematics
Solve
304 30 -
= 9
1107
Solved
Show answers
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Ответ:
Solve
304 30 -
= 9
1107
Step - by - step explanationОтвет:
9514 1404 393
∠PAO = 90°∠APO = 30°∠AOB = 120°PB ≈ 8.7Step-by-step explanation:
A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.
OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.
__
As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.