:HL["https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/162/image8-u2kRwqnnPvkQfv4HkiROWCjeJmm08a.png","image"] :HL["https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/162/image11-4J8OMvYq5ZmFQ6D5P5T4d2TodeFl5j.png","image"] :HL["https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/162/image12-LADMWCN0je5QaqpVfmSPUiVza9L19k.png","image"] :HL["https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/162/image16-vayUnkK6TfTWiKIafp6DQsAp1ehHNY.png","image"] 29:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

5

"}}] 2a:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

7

"}}] 2b:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

9

"}}] 2c:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

11

"}}] 2f:["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}}

"}}] 85:Tc92,

\left| {\vec{\mathrm{OP}}} \right|

30:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$85"}}] 31:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{O}}

"}}] 86:T506,

\displaystyle \frac{8}{3}

32:["$","span","p0-0-t0-m11",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$86"}}] 33:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

3

"}}] 87:T509,

\displaystyle \frac{10}{3}

34:["$","span","p0-0-t0-m15",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$87"}}] 88:T509,

\displaystyle \frac{11}{3}

35:["$","span","p0-0-t0-m17",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$88"}}] 36:["$","span","p0-0-t0-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

4

"}}] 89:Tff2,

\displaystyle \frac{x ^{2}}{48} + \frac{y ^{2}}{4 b ^{2}} = 1

38:["$","span","p0-0-t0-m5",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$89"}}] 39:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

1

"}}] 3a:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}} \\left( 6 , b \\right)

"}}] 3b:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}] 3c:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

y

"}}] 3d:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{A}}

"}}] 3e:["$","span","p0-0-t0-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{B}}

"}}] 8a:Td4b,

\displaystyle {\overline{\mathrm{PF}}} + {\overline{{\mathrm{PF}}'}} = {\overline{\mathrm{AB}}}

3f:["$","span","p0-0-t0-m19",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$8a"}}] 8b:T47e,

b ^{2} \times c

40:["$","span","p0-0-t0-m21",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$8b"}}] 41:["$","span","p0-0-t0-m23",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

20

"}}] 42:["$","span","p0-0-t0-m25",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

24

"}}] 43:["$","span","p0-0-t0-m27",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

28

"}}] 44:["$","span","p0-0-t0-m29",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

32

"}}] 45:["$","span","p0-0-t0-m31",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

36

"}}] 46:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

m

"}}] 47:["$","span","p0-0-t0-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{B}}

"}}] 48:["$","span","p0-0-t0-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{C}}

"}}] 8c:Ta66,

\displaystyle {\overline{\mathrm{AB}}} = 2 \sqrt{3}

49:["$","span","p0-0-t0-m21",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$8c"}}] 8d:T54b,

\displaystyle {\overline{\mathrm{AC}}} = 2

4a:["$","span","p0-0-t0-m23",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$8d"}}] 8e:T54b,

\displaystyle {\overline{\mathrm{PA}}} = 5

4b:["$","span","p0-0-t0-m25",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$8e"}}] 4c:["$","span","p0-0-t0-m27",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{ABC}}

"}}] 4d:["$","span","p0-0-t0-m29",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{PBC}}

"}}] 4e:["$","span","p0-0-t0-m31",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{B}}

"}}] 4f:["$","span","p0-0-t0-m33",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{A}}

"}}] 50:["$","span","p0-0-t0-m35",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{C}}

"}}] 51:["$","span","p0-0-t0-m37",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{A}}

"}}] 8f:T9e3,

\displaystyle \frac{\sqrt{3}}{3}

52:["$","span","p0-0-t0-m39",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$8f"}}] 90:T9e3,

\displaystyle \frac{\sqrt{6}}{2}

53:["$","span","p0-0-t0-m41",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$90"}}] 91:T6b9,

\displaystyle \sqrt{3}

54:["$","span","p0-0-t0-m43",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$91"}}] 92:T6e0,

\displaystyle 2 \sqrt{2}

55:["$","span","p0-0-t0-m45",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$92"}}] 93:Ta17,

\displaystyle \frac{4 \sqrt{6}}{3}

56:["$","span","p0-0-t0-m47",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$93"}}] 57:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-1-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/162/image8-u2kRwqnnPvkQfv4HkiROWCjeJmm08a.png","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"75cqw"}}]]}] 5a:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{CD}}

"}}] 5b:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}}

"}}] 5c:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{ABCD}}

"}}] 5d:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{Q}}

"}}] 94:T1b94,

{\vec{\mathrm{PA}}} \bullet {\vec{\mathrm{PQ}}} = \left| {\vec{\mathrm{PQ}}} \right| ^{2}

5e:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["(가) ",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$94"}}],"\n(나) ","$L95",""]}] 96:T1c8c,

\left( {\vec{\mathrm{AR}}} + {\vec{\mathrm{QR}}} \right) \bullet \left( {\vec{\mathrm{PR}}} + {\vec{\mathrm{QR}}} \right) = 0

5f:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-2-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$96"}}],"을 만족시키는 점 ","$L97","에 대하여\n","$L98","의 최댓값을 ","$L99",", 최솟값을 ","$L9a","이라 할 때, ","$L9b","의 값은? [4점]\n① ","$L9c","\n② ","$L9d","\n③ ","$L9e","\n④ ","$L9f","\n⑤ ","$La0",""]}] 60:["$","p","p0-3",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-3-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/162/image11-4J8OMvYq5ZmFQ6D5P5T4d2TodeFl5j.png","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"50cqw"}}]]}] a1:Ta9f,

2026년-07월-고3-수학문제(기하)