st","extracted_subject":"MATH","extracted_chapter":"CIRCLE AND SYSTEM OF CIRCLES","extracted_topic":"TANGENT AND NORMAL TO A CIRCLE","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1803.png?top_left_x=0&top_left_y=1457&width=532&height=319&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e70425d76b7ab31d9da","slug":"the-length-of-the-transversal-common-tangent-to-th","content":"The length of the transversal common tangent to the circle\n\nx² + y² = 1 and (x –t)² + y² = 1 is \\(\\sqrt{21}\\), then t is equal to-","options":[{"_id":"68a39c897f15af4716bb9a5f","text":"± 2","sequence":0,"isCorrect":false},{"_id":"68a39c897f15af4716bb9a60","text":"±5","sequence":1,"isCorrect":true},{"_id":"68a39c897f15af4716bb9a61","text":"±3","sequence":2,"isCorrect":false},{"_id":"68a39c897f15af4716bb9a62","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"±5","explanation":"C₁ (0, 0) r₁ = 1\n\nC₂ (t, 0) r₂ = 1\n\n![](https://cdn.pureessence.tech/canvas_475.png?top_left_x=534&top_left_y=0&width=300&height=210)\n\nPQ = 2\\(\\sqrt{PT_{1}}\\) = 2 \\(\\sqrt{\\frac{t^{2}}{4} - 1}\\)= \\(\\sqrt{21}\\)\n\n\\(\\sqrt{t^{2} - 4}\\)= \\(\\sqrt{21}\\)\n\nt² = 25 ή t = ±5","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:36.918Z","__v":0,"vector_store_id":"a38bfbf8-893f-4cd8-8a19-38609e605c1e","updated_at":"2024-08-30T21:49:36.918Z","isStarred":false},"params":{"questionSlug":"the-length-of-the-transversal-common-tangent-to-th"}}]}]]

Question: The length of the transversal common tangent to the circle x<sup>2</sup> + y<sup>2</sup> = 1 and (x...

Solution