## Well-spoken by Miles

### Puzzle explanation

The letters omitted from wordplay spelt “Euler line”.
The three occurrences of X in the grid
were the vertices of a tall scalene triangle.
The preamble phrase LONE TEPEE LEANS
(a jumble of the unclued entries ÉLAN, STEP, LEO, EEN)
hinted at this triangle’s shape.
The nine occurrences of O marked
the defining points of the triangle’s nine-point circle:
the mid-points of the sides,
the feet of the altitudes
(where a line from a vertex meets the opposite side at a right angle),
and the mid-points along the altitudes
between the vertices and the orthocentre
(where the three altitudes meet).
In the centre of the circle
(the shape both delineated by Os and resembling an O),
a fourth X was added to mark the “nine-point centre”,
at the cell corner between
the L of LIANA and the P of IN PERSON.
The Euler line had to be drawn
parallel to the triangle’s right-hand side
and passing through this X
(*beside* the spaced out letters of EULER,
not through their cell centres).
The puzzle’s title cryptically referred to
Euler as a homophone of “oiler”,
an oil well.

### Clue explanations

Conventions: * = anagram, < = reversal

Answer (unclued letter) |
Explanation |

BEAUXITE | BÊTE around (A + UZI with X for Z) |

ETEN | ET + EN; the de Longchamps point is also on the Euler line |

NASUTE | SAN < + UTE |

BENIGHTM(E)NT | (MIGHTN’T BE) * around N |

UNEQUALS | ALS after (UNE + QU) |

KEFIR | (E(gg) F(ermented)) in KIR |

TENACE | TEN + ACE (flanking J, Q, K) |

SO(U)PER | SOPER; ref. Donald Soper |

DECOL(L)ATORS | DECORATORS with L for R |

CATNEP | (PET CAN) * |

APOGEE | APE(x) around (O + GE) |

LIANA | (A + NAIL) < |

IN PERSON | IN + PER + SO + N |

NEAR-SIGHTED | (IN + NEAR-SIGHTED) * = DISHEARTENING |

(E)SLOIN | NOILS * |

SOLE | 2 meanings; E after SOL |

TANDOORS | ROAST * around (ND + O’) |

(R)EBUKED | BE < + UK + ED |

CTENE | C + TENE |

BENEFACTOR | (ROT + CAFÉ + NEB) < |

AUGURA(L) | (ARUGULA − L) < |

UNHATS | HAUNTS with first two letters moved to the middle |

(I)SMS | SMS |

ETNA | 2 meanings |

LETHE | LIFE − IF + THE |

CAPOTASTOS | CAPO + TAST(e) + O’ + S |

NUTS | NU + T(ank)S |

CERE | SINCERE − SIN |

LEAP | 2 meanings |

NONG | SONG with N for S |

ALLEGRO | (liber)AL LEGRO(om) |

SPANDEX | SPAN + homophone of DECKS |

PEPINO | PEP + (ON + I) < |

AN(N)EX | NE in AX |

NOEL(E) | “lover” with NO EL = “over” |

BEST | 3 meanings |

IRON | I + RN around O |

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