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Omni-MATH / Let the circles k₁ and k₂ intersect at two points A and B , and let t be a common tangent of k₁ and k₂ that touches k₁ and k₂ at M and N respectively. If t⊥AM and MN=2AM , evaluate…

Problem

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problem

Let the circles

k_1

and

k_2

intersect at two points

A

and

B

, and let

t

be a common tangent of

k_1

and

k_2

that touches

k_1

and

k_2

M

and

N

respectively. If

t\perp AM

and

MN=2AM

, evaluate the angle

NMB

Plain-text mathematical notation (without MathML)

Let the circles k₁ and k₂ intersect at two points A and B , and let t be a common tangent of k₁ and k₂ that touches k₁ and k₂ at M and N respectively. If t⊥AM and MN=2AM , evaluate the angle NMB .

Original LaTeX notation

Let the circles $k_1$ and $k_2$ intersect at two points $A$ and $B$ , and let $t$ be a common tangent of $k_1$ and $k_2$ that touches $k_1$ and $k_2$ at $M$ and $N$ respectively. If $t\perp AM$ and $MN=2AM$ , evaluate the angle $NMB$ .

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task_id: 8c9703d3-c1a3-50ee-84ad-0d2838138043
task_key: test--8c9703d3-c1a3-50ee-84ad-0d2838138043
task_revision_id: 4
config / split: / test

Official source

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