Geometry Problem 1547. Post your solution in the comment box below.

Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Let BD cut the circle at E. Let F be the midpoint of BE. Let BF = y and OF = z

ReplyDeleteOFDC is a Rectangle. Triangles OBF & ABD are similar

So 4/5 = y/(5-z) = z/(y+4) which gives z = 4(y+4)/5

Substituting for z, y/(5 - 4(y+4)/5)) = 4/5

Simplifying y = 36/41

Therefore BD = 4 + 36/41 = 4.89 approximately

Sumith Peiris

Moratuwa

Sri Lanka

From right triangle OBA, tan(angleBAO) = 4/5, so BAO = atan(4/5)

ReplyDeleteNow, BAC = 2 BAO and from right triangle BDA,

BD = 5 sin(BAC) = 5 sin(2*atan(4/5) = 4.878

Christos