The length of the minute hand is 200% of the length of the hour hand. in 1 hour, how much farther does the tip of the minute hand move than the tip of the hour hand? round your answer to the nearest hundredth. (the length of the hour hand is 20mm)

230/6

This is because each circumference is equal to 2r. So the distance the minute hand would travel would be 40. Then the minute hand would have a circumference of 20. However, you would have to divide that by 12 since it only traveled 1/12th of the distance around. 

When you subtract the hour hand's distance from minute hand's distance, you get the answer above. 

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12