Question #00f2d Geometry Circles Central, Inscribed, and Circumscribed Angles 1 Answer CW Apr 8, 2017 #r=sqrt(7/3)# Explanation: I assume that #AB=BC=CD=1, and DE=EF=FA=2# As shown in the diagram, #3(x+y)=360^@ => x+y=120^@# #w=(180-x)/2, z=(180-y)/2# #=> w+z=(360-(x+y))/2=(360-120)/2=120^@# In #DeltaCDE#, #CE^2=CD^2+DE^2-2(CD)(DE)cos(w+z)# #CE^2=1^2+2^2-2*1*2*cos120=7# In #DeltaOCE#, #CE^2=OC^2+OE^2-2(OC)(OE)cos(x+y)# #7=r^2+r^2-2r^2cos120# #=> 7=2r^2(1-cos120)=2r^2(1-(-1/2))=3r^2# #=> r^2=7/3# #=> r=sqrt(7/3)# Answer link Related questions Why perpendicular bisectors of any triangle intercept in the center of circumscribed circle? What is the area of a semicircle with radius #8# cm? If one of the sides of a right angled triangle, whose all sides have integral values, is #12#,... Prove that the largest isosceles triangle that can be drawn in a circle, is an equilateral triangle? Question #af2a7 Question #19822 ABC is a Right Triangle ,right angled at B. C(o,r) is the incircle and o is the incenter of the... Damari is constructing an equilateral triangle inscribed in a circle and has gotten this far.... This figure shows circle O with diameter QS . mRQS=290∘ What is the measure of ∠ROS ? This figure shows circle A with inscribed ∠RSQ . m∠RSQ=24° What is the measure of RSQ? See all questions in Central, Inscribed, and Circumscribed Angles Impact of this question 2373 views around the world You can reuse this answer Creative Commons License