!["Teladoc Health Moves Headquarters to Marx Realty Tower from Westchester" # 2006 AMC 12B Problems/Problem 6. (Redirected from 2006 AMC 12B Problem 6) ## Problem. A circle of radius $r$ is inscribed in a right triangle with sides $3$, $4$, and $5$ so that the circle is tangent to both legs. What is the value of $r$? $text {(A) } frac{3}{2} qquad text {(B) } frac{4}{3} qquad text {(C) } frac{5}{4} qquad text {(D) } frac{12}{5} qquad text {(E) } frac{5}{2}$ ## Solution. [asy] unitsize(0.5cm); defaultpen(0.8); pair A=(0,0), B=(4,0), C=(4,3), D=(0,3), E=(4/5,3/5), F=(3,0), G=(0,4), H=(0,5), I=(3,4), J=(](https://cremarketbeat.com/wp-content/uploads/2025/01/10-Grand-Central-7866-Edit-1.jpg)
“Teladoc Health Moves Headquarters to Marx Realty Tower from Westchester” # 2006 AMC 12B Problems/Problem 6. (Redirected from 2006 AMC 12B Problem 6) ## Problem. A circle of radius $r$ is inscribed in a right triangle with sides $3$, $4$, and $5$ so that the circle is tangent to both legs. What is the value of $r$? $\text {(A) } \frac{3}{2} \qquad \text {(B) } \frac{4}{3} \qquad \text {(C) } \frac{5}{4} \qquad \text {(D) } \frac{12}{5} \qquad \text {(E) } \frac{5}{2}$ ## Solution. [asy] unitsize(0.5cm); defaultpen(0.8); pair A=(0,0), B=(4,0), C=(4,3), D=(0,3), E=(4/5,3/5), F=(3,0), G=(0,4), H=(0,5), I=(3,4), J=(
Marx Realty has announced that Teladoc Health, a leading telemedicine company, will be expanding and extending its lease at 10
Steve Griffin
January 24, 2025
!["Maryland Retail Center Sold for $10M by CRC Brokers" # 2006 AMC 12B Problems/Problem 6. (Redirected from 2006 AMC 12B Problem 6) ## Problem. A circle of radius $r$ is inscribed in a semicircle. The semicircle is then inscribed in a square. What is the ratio of the area of the circle to the area of the square? $text {(A) } frac{pi}{8}qquad text {(B) } frac{pi}{6}qquad text {(C) } frac{pi}{4}qquad text {(D) } frac{pi}{3}qquad text {(E) } frac{pi}{2}$ ## Solution. [asy] unitsize(1cm); defaultpen(0.8); real r=1; pair A=(-1,0), B=(1,0), C=(0,1), D=(0,-1), O=(0,0); draw(A--B--C--cycle); draw(arc(O,r,0,180)); draw(O--(0.707,0.707)); label](https://cremarketbeat.com/wp-content/uploads/2025/01/CRC_Govenors.jpg)
