Question 1:
To find angle POF, we need to apply the tangent-secant angle theorem, which states that the measure of an angle formed by a tangent and a secant intersecting at the point of tangency is equal to half the measure of its intercepted arc.
Given that angle PEO is 46°, we can find angle POF using the intercepted arc PO.
Since angle POF is an inscribed angle intercepting arc PO, we have:
angle POF = 1/2 * arc PO
Since angle PEO is given as 46° and it subtends arc PO, arc PO will be twice this measure, which is 92°.
Now, we can find angle POF:
angle POF = 1/2 * 92°
angle POF = 46°
Therefore, angle POF is 46°.
Question 2:
To find the length of AP, we can use the Pythagorean theorem in triangle APT.
Given:
PT = 2.000 in.
ET = 1.200 in.
PO = 0.614 in.
Diameter = 2.620 in.
We can first find the length of AE using the Pythagorean theorem:
AE^2 = AP^2 + PE^2
AP^2 = AE^2 - PE^2
Given that PO is the radius and the diameter is 2.620 in, we can find the length of AE:
AE = Diameter - PO
AE = 2.620 in - 0.614 in
AE = 2.006 in
Now, we can find the length of AP:
AP^2 = 2.006^2 - 1.200^2
AP^2 = 4.024 - 1.440
AP^2 = 2.584
Taking the square root of both sides to solve for AP:
AP ≈ √2.584
AP ≈ 1.606 in
Therefore, the length of AP is approximately 1.606 inches.
