See complete Problem 154

Triangle, Inradius, Circumradius, Chord. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Sunday, August 3, 2008

### Elearn Geometry Problem 154

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## Sunday, August 3, 2008

###
Elearn Geometry Problem 154

## Link List

Online Geometry theorems, problems, solutions, and related topics.

See complete Problem 154

Triangle, Inradius, Circumradius, Chord. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

Subscribe to:
Post Comments (Atom)

1)in triangle DIC

ReplyDeleteang(DIC)=ang(BDC)=ang(BAC)=A;inscribed angles with endpoints B and C

the lines BI and CI are bissectors ang(DIC)=(B+C)/2;ang(ICD)=A+B+C-A-(B+C)/2=(B+C)/2

triangle DIC is isoscele DI=DC

2)with the law of sines

in triangle IBC: BC sin(C/2)=IB sin((B+C)/2)

in triangle IDC: IC sin((B+C)/2)=ID sinA

in triangle ABC: BC= 2RsinA and r= ICsin(C/2)

therefore 2Rr=IB.ID

other questions related to this configuration

ReplyDeletea) prove that D is the circumcenter of triangle AIC

b)lines AI,CI intersect the circumcercle of ABC at E and F.

Prove that I is the orthocenter of DEF

(1) Since BD bisects angle B, D is the midpoint of arc ADC. Therefore B/2 = CAD = ACD, and ICD = C/2 + ACD = C/2 + B/2. On the other hand, DIC = IBC + BCI = B/2 + C/2. Hence DIC is isosceles and DI = CD.

ReplyDeletehttp://ahmetelmas.wordpress.com/2010/05/15/geo-geo/

ReplyDeletehttp://img208.imageshack.us/img208/1433/respuesta154.png

ReplyDelete