Question

Triangle abc with right angled at b has bc=6 and ac=12 a semicircle inscribed in the triangle has its diameter on ab and is tangent to ac at p find the ratio of the region apo to the area of the region pcb

Answer 1

 can reflect triangle  over line  This forms the triangle  and a circle out of the semicircle. Let us call the center of the circle 

We can see that Circle  is the incircle of We can use the formula for finding the radius of the incircle to solve this problem. The area of  is  The semiperimeter is Simplifying  Our answer is therefore