on the horns of a dilemma

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top: white rhinoceros and bighorn sheep
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1. One of the hard, usually permanent structures projecting from the head of certain mammals, such as cattle, sheep, goats, or antelopes, consisting of a bony core covered with a sheath of keratinous material.
2. A hard protuberance, such as an antler or projection on the head of a giraffe or rhinoceros, that is similar to or suggestive of a horn.
a. The hard smooth keratinous material forming the outer covering of the horns of cattle or related animals.
b. A natural or synthetic substance resembling this material.
4. A container, such as a powder horn, made from a horn.
5. Something having the shape of a horn, especially:
a. A horn of plenty; a cornucopia.
b. Either of the ends of a new moon.
c. The point of an anvil.
d. The pommel of a saddle.
e. An ear trumpet.
f. A device for projecting sound waves, as in a loudspeaker.
g. A hollow, metallic electromagnetic transmission antenna with a circular or rectangular cross section.
6. Music
a. A wind instrument made of an animal horn.
b. A brass instrument, such as a trombone or tuba.
c. A French horn.
d. A wind instrument, such as a trumpet or saxophone, used in a jazz band.
a. A usually electrical signaling device that produces a loud resonant sound: an automobile horn.
b. Any of various noisemakers operated by blowing or by squeezing a hollow rubber ball.
8. Slang A telephone.
intr.v. horned, horn·ing, horns
To join without being invited; intrude. Used with in.
blow/toot (one's) own horn Informal
To brag or boast about oneself.
draw/haul/pull in (one's) horns Informal
1. To restrain oneself; draw back.
2. To retreat from a previously taken position, view, or stance.
3. To economize.
on the horns of a dilemma
Faced with two equally undesirable alternatives.

[Middle English, from Old English; see ker- in Indo-European roots.]

horn adj.
horn′ist n.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

on the horns of a dilemma

In a situation in which a difficult choice must be made, often between two equally unpleasant options.
Dictionary of Unfamiliar Words by Diagram Group Copyright © 2008 by Diagram Visual Information Limited
References in periodicals archive ?
The Fed could be caught on the horns of a dilemma however, if the tariffs boost prices such that policymakers have to weigh rising inflation with slowing growth.
It seems that you are, once again, on the horns of a dilemma -- this time over whether to send your colt Cracksman for the Prix de l'Arc de Triomphe at Chantilly a fortnight tomorrow.
AN auctioneer is on the horns of a dilemma - over the sale of a stuffed rhinoceros head worth at least pounds 30,000 to Chinese herbalists.