In the acute angle B, there are five adjacent circumscribed unequal circles, all of which are tangent to the edge of angle B (the radii are arranged from small to large). The radii are R1, R2, R3, R4 and R5 respectively. If the minimum radius R1 = 1, the maximum radius R5 = 81. Find the degree of angle B The angle is 60 degrees, I know. What I want is the proof process

It is known that
r1:r2:r3:r4:r5=1:3:9:27:81
Draw a picture by yourself
The ratio of opposite side to bevel side is 1:2
Therefore, B = 60 degree
The key point of this problem is that we must understand the proportion of these five radii and prove it concretely

Ask a few math questions, step by step
1. In space quadrilateral ABCD, E F G is on AB BC CD respectively, and AE: EB = CF: FB = 2, CG: GD = 3. Through E F G, we make a plane intersection ad at h, and prove that EH FG BD three lines intersect at a point
2. Cut a cone into a frustum. The radius ratio of the top and bottom surfaces of the frustum is known to be 1:4, and the generatrix length is 10cm. Calculate the generatrix length of the cone
3. In the cube abcd-a1b1c1d1, eg / / plane bdd1b1 is the focus of BC c1d1

Let eh ∩ FG = P, then p ∈ EH. Let eh, FG and BD have the same point. 2. Let ∩ eh, FG and BD have the same point

Class 1, grade one of a junior high school, organized students to go to the park. There were 50 students in the class organized boating activities. 1. They rented 10 boats, and each boat was full of people. How many boats did they rent? 2. How much did they spend on renting a boat? A three digit number, the number on the hundred is one more than the number on the ten, and the number on the one is two times less than the number on the ten, If the order of the three digits is reversed, the sum of the three digits and the original three digits is 1171

1. Solution: let the big boat rent x, the small boat rent 10-x, 6x + 4 (10-x) = 50 6x + 40-4x = 50 2x = 10, x = 5, the small boat rent 10-5 = 5, they cost 5 * 10 + 5 * 8 = 5 (10 + 8) = 90 yuan. 2

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