Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the diagram below for more details.
Join B to O Fröm pythagora theorem r2 = 3/2 sq2R (tr BEO and BDE) The same r3 = 1/2sq10RFrom similar tr BDE and BHF we get BH = 3sq5
http://s29.postimg.org/8hhggawgn/pro_1159.pngLet R= radius of circle OWe have ∡ (BHD)= ∡ (BHF)=90 => D, H, F are collinearDB^2= DẸ 2R = 18.RBF^2= FG. 2R= 10.RDB/ BF= sqrt(18/10)= sqrt(1.8)Observe that F is the midpoint of arc BC so∡ (CBF)= ∡ (BDF)= angle A/2So triangle BDH simillar to FBGDB/BF= BH/FG = sqrt(1.8)BH= 5 x sqrt(1.8)= 3.sqrt(5)
Tr.s BDE and BHF are similar soBD/BF = 9/BH ....(1)Tr. s BDH and BGF are similar soBD/BF = BH/5 ....(2)From (1) and (2), 9/BH = BH /5 Hence BH = 3sqrt5Sumith PeirisMoratuwaSri Lanka