Answer:
1. r = 7√2 dm ≈ 9.90 dm
2. ∠ENK = 50°; ∠KEG = 59°
Step-by-step explanation:
1. If ∠A is 90°, then the angle at O that is opposite is also 90°, hence the tangent lines and radii make a square. The diagonal of the square (OA) is 14 dm, so the side length, the radius, will be 14/√2 dm = 7√2 dm.
__
2. The length of chord EK is the same as the length of chord VG, so arc EK is the same measure as arc GV, namely 50°. The measure of ∠ENK is the average of the measures of arcs EK and GV, so is also 50°.
∠EGK = 25°, since it is half the measure of arc EK. The sum of the angles in ΔKEG is 180°, so we have ...
∠EKG + ∠EGK + ∠KEG = 180°
∠KEG = 180° - 96° -25° = 59°
