Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to view more details of problem 1244.

## Saturday, August 13, 2016

### Geometry Problem 1244: Circle, Radius, Perpendicular, Chord, Secant, Measurement. Mind Map

Labels:
chord,
circle,
measurement,
mind map,
perpendicular,
radius,
secant

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https://goo.gl/photos/FGTGW9iSkgxRKfx16

ReplyDeleteConnect BF, BC and BD

Note that C is the midpoint of arc BG

Triangle BEC similar to FBC ( case AA)

So CB^2=CE.CF

Triangle DCB similar to BCA ( case AA)

So CB^2=CD.CA

And CE.CF=CD.CA or 4x 10= 3(x+3)

So x= 31/3

Let AB cut the circle at G.

ReplyDeleteIn isoceles Tr. BCG,

CG^2 - CE^2 = BE.GE = CE.EF = 24

So CG^2 = 24 + 16 = 40

Now < CGB = CBG = < GDA

Hence < CGD = < DGB - < CGB = < DGB - < GDA = < GAD

Hence CG^2 = CD.CA

So 40 = 3(3+x) from whence x = 31/3

Sumith Peiris

Moratuwa

Sri Lanka

2nd solution

ReplyDelete< CFD = < CGD = < EAD as before

Hence AFED is cyclic and the result is easily calculated

Sumith Peiris

Moratuwa

Sri Lanka