SOLUTION: 1. if a circle is inside a trapazoid(touching its sides) with one base 45 and the other base 125. what is the diameter of the circle? 2. you have 2 circles touching each other

Question 30573: 1. if a circle is inside a trapazoid(touching its sides) with one base 45 and the other base 125. what is the diameter of the circle?

2. you have 2 circles touching each other at one point. one circle is 6ft. the other is 18ft. whats the shortest length of cord that will go around both circles?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
REFER FOLLOWING DIAGRAM

LET RADIUS OF CIRLE =R=OQ=OT
LET ST=X
TRIANGLES STD AND SQA ARE SIMILAR..SO
(X+2R)/62.5=X/22.5......(X+2R)/X=62.5/22.5.....2R/X=40/22.5......R/X=20/22.5=8/9
R/8=X/9=K SAY....R=8K....X=9K....
D IS AN EXTERNAL POINT TO CIRCLE AND HENCE 2 TANGENTS FROM IT ARE EQUAL..THAT IS
DU=DT=22.5
SIMILARLY
AU=AQ=62.5
IN RIGHT ANGLE TRIANGLE DAP
DA^2=DP^2+AP^2
(62.5+22.5)^2=(2R)^2+40^2
4R^2=85^2-40^2
R=37.5
HENCE DIAMETER OF CIRCLE =75.
THE SECOND QUESTION IS NOT CLEAR..CAN YOU PLEASE GIVE A SKETCH...
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