1.Two semicircles of radius 6 units are inscribed in a semicircle of radius 12 units. A circle is inscribed so that it is tangent to all three semicircles. Find the circumference of the circle
2. In triangle ABC, AB=260, AC=400, and BC=520. Point D is chosen on BC so that the circle inscribed in triangle ABD and ADC are tangent to AD at the same point. What is the length of BD?
I've marked the right triangle I use for my calculations (see attachment)
Collect like terms and separate the variable and the constants on different sides of the equation:
The original question asked to calculate the circumference of the tangent circle. Since you know the radius you can use the formula:
Plug in the value of r and you'll get: