2007-04-17 20:26:24 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Their centers are 34 cm apart. The radii are each perpendicular to the common external tangent. You can form a rectangle by drawing the perpendicular from the center of little circle to radius of larger circle. This rectangle has sides x and 9, where x is the common external tangent. This also forms a right triangle with legs 16 and x and hypotenuse 34. That's how you find x:
x² + 16² = 34²
x = 30 cm = length of common external tangent
2007-04-18 03:02:03 · answer #1 · answered by Kathleen K 7 · 1⤊ 0⤋
The length of common tangent of circle with radius 9 cm is 16.744cm
The length of common tangent of circle with radius 25 cm is 46.744cm
2007-04-19 17:55:24 · answer #2 · answered by Alyssa 2 · 0⤊ 0⤋
The length of common tangent of circle with radius 9 cm is 16.744cm
The length of common tangent of circle with radius 25 cm is 46.744cm
2007-04-17 23:24:29 · answer #3 · answered by Vatsal S 2 · 0⤊ 0⤋
We have similar right triangles.
The hypotenuses are:
r = 9 + x
R = 25 + 2*9 + x = 43 + x
The short legs are:
r
R
The long legs are:
z
Z
We want to solve for Z - z.
By similar triangles
(9 + x)/9 = (43 + x)/25
25x + 225 = 9x + 387
x = 81/8
Also by similar triangles
z/9 = (Z + z)/25
25z = 9Z + 9z
16z = 9Z
Z = (16/9)z
z² = (9 + x)² - 9² = (9 + 81/8)² - 81 = (153/8)² - 81
z² = 81[(17/8)² - 1] = (81/64)(289 - 64) = (81/64)(225)
z = (9/8)(15) = 135/8
Z - z = (16/9)z - z = (7/9)z = (7/9)(135/8) = 105/8 cm
2007-04-17 21:46:22 · answer #4 · answered by Northstar 7 · 0⤊ 1⤋
d^2+(25-9)^2=(25+9)^2. So d=30.
2007-04-17 21:25:58 · answer #5 · answered by gianlino 7 · 0⤊ 0⤋
Formula is D^2=(R+r)^2+(R-r)^2
i.e.
d=30
it is done by forming a right angled triangle by 1 radius ,tangent ,and 2 radii joined together
and applying PGT in left over.....
2007-04-17 23:44:15 · answer #6 · answered by Somebody 2 · 0⤊ 0⤋
Gudspeling is actual. And he has a link to an fantastically astounding diagram. the only distinction is that in the time of the surely subject the two circles are externally tangent. yet that basically makes it extra convenient to calculate the hypotenuse of the appropriate triangle.
2016-10-22 12:00:42 · answer #7 · answered by ? 4 · 0⤊ 0⤋
√[(25-9)^2+(25+9)^2]=√(256+1,156)=√1,412cm
2007-04-17 20:36:39 · answer #8 · answered by Anonymous · 1⤊ 0⤋
Can't unless you tell us how far apart the centers are.
Or are you saying they are tangential and the centers are 31cm apart?
2007-04-17 20:32:24 · answer #9 · answered by Orinoco 7 · 1⤊ 2⤋