Two circles of radius r1 and r2 are extenally tangential to each other and are also externally tangential to a staight line l. Another circle of some unknown radius is externally tangential to both the circles and to the straight line l. Find the adius of that circle.
To find the radius of the unknown circle, let's break down the problem into smaller steps and use the property of tangency.
Step 1: Draw the diagram
Start by drawing two circles with radii r1 and r2 that are externally tangent to each other and to a straight line l.
r1
●----○■---○----●
/ \
/ \
/ \
●○■-------------●
r2 l
Step 2: Find the distance between the centers of the two circles
The distance between the centers of the two circles can be found by summing the radii of the circles and then subtracting it from the distance between the centers of the two circles.
Let's denote the distance between the centers of the two circles as d.
d = (r1 + r2)
Step 3: Find the distance between the centers of the unknown circle and the straight line l
Since the unknown circle is externally tangent to the straight line l, the distance between the centers of the unknown circle and the straight line is equal to the radius of the unknown circle.
Let's denote the radius of the unknown circle as r.
r = d - r1 - r2
Step 4: Calculate the radius of the unknown circle
Substitute the value of d from step 2 into step 3 to find the radius of the unknown circle.
r = (r1 + r2) - r1 - r2
r = r1 + r2 - r1 - r2
r = 0
The radius of the unknown circle is 0.
Explanation: Since the two circles are externally tangent to each other and to the straight line l, the unknown circle would be infinitely small and have a radius of 0.