What’s My Line by Mr E

Puzzle explanation

In some across clues, the wordplay gave the answer with a letter replaced by X, and in others by Y. The correct X letters could be arranged as SEPT and those given as Y made UN, so the first co-ordinate was (7, 1). Likewise, down clues had X for TWO and Y for TEN, giving (2, 10). Using the lower-left corner of the grid as the origin of a coordinate plane, the line segment connecting the two points passed through the letters of COGITO ERGO SUM. The letters of RENÉ DESCARTES (which is a jumble of ENTERED ACROSS with É instead of O) could be found on the congruent line segment connecting (12, 3) and (7, 12).

Clue explanations

Conventions: * = anagram, < = reversal

No Answer Explanation [wrong letter]
Across
1 CHAPATI CHAP + AT(e) + I(t)
8 ASTI (ASTI in TEST) = TASTIEST
12 RECON RE + C + ON
13 NEED-BE homophone of KNEAD BEA
14 ORGA[N]ZINE FOR + GA[Y] + ZINE − F
15 COOL-HEADED COOED around (H in LEAD)
16 INSULSE (UNLESS I) *
17 DRAG ’D + RAG
18 FATTY FR + ATTY − R
20 AVARICE CAVIARE *
21 REGIMENTS ’RE + MEN in GITS
25 MACRONS M + CARS * around ON
27 [P]ARER [X] + ARE + R
29 IRON I + ON after R
30 CHINE[S]E E[X] in CHINE
32 SEMPER IDEM (RIDE + M) after (MP in SEE)
33 UNNOTICED (NOT ICED) after (J)UN(e)
34 T[U]PELO L(ettuce) in (T[Y]PE + O’)
35 CH[E]AT TA[X] < after CH
36 THAW WHAT *
37 ASTAR[T]E STAR in A[X]E
Down
1 CRUCIFY (CUR < + I + F(ound)) in CY
2 HERON HERO + N(o)
3 ACCOST ACT around COS
4 POLLU[T]E POLLU[X] + E
5 THRESHING MILL spoonerism of MESHING THRILL
6 HEAD [O]VER HEELS (SLAVE HE[X]ED HER) *
7 SE[N]ECAN SCAN around E[Y]E
9 SBIRRI (I + R + RIBS) <
10 TENTACLE (A CLUE) after TENT − U
11 ICE AGE I + E in CAGE
19 AMARAN[T]H (AN[Y] HARM) * after A
22 GORE-TEX (GORE-TEX + IN HEAT + RAIN) * = (A HIT + GENERATION XER) *
23 TANI[W]HA (A + HAT) < around NI[X]
24 CR[E]MATE CR[Y] + MATE
25 MINUET TUNE * after MI
26 CORNUA CORA around NU
28 REDDER SHREDDER − SH
31 SEBAT B in SEAT
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