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Omni-MATH / Let ABC be an isosceles triangle with AC=BC , let M be the midpoint of its side AC , and let Z be the line through C perpendicular to AB . The circle through the points B , C , and…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let

ABC

be an isosceles triangle with

AC=BC

, let

M

be the midpoint of its side

AC

, and let

Z

be the line through

C

perpendicular to

AB

. The circle through the points

B

C

, and

M

intersects the line

Z

at the points

C

and

Q

. Find the radius of the circumcircle of the triangle

ABC

in terms of

m = CQ

Plain-text mathematical notation (without MathML)

Let ABC be an isosceles triangle with AC=BC , let M be the midpoint of its side AC , and let Z be the line through C perpendicular to AB . The circle through the points B , C , and M intersects the line Z at the points C and Q . Find the radius of the circumcircle of the triangle ABC in terms of m=CQ .

Original LaTeX notation

Let $ABC$ be an isosceles triangle with $AC=BC$ , let $M$ be the midpoint of its side $AC$ , and let $Z$ be the line through $C$ perpendicular to $AB$ . The circle through the points $B$ , $C$ , and $M$ intersects the line $Z$ at the points $C$ and $Q$ . Find the radius of the circumcircle of the triangle $ABC$ in terms of $m = CQ$ .

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task_id: db04fbb2-778a-5cc0-b14d-d00ad183a76f
task_key: test--db04fbb2-778a-5cc0-b14d-d00ad183a76f
task_revision_id: 4
config / split: / test

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