Find the length of Tangent TP | Maths | Circles and Tangents | IMO Olympiad

Watch full video to view as how Theoram for Tangents to Circle is used to find the length of tangent TP to the circle.

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[santiagoarosam]

TO is the axis of symmetry of the proposed figure and also the perpendicular bisector of the chord PQ → ∆TPO is a right triangle since the tangent TP is perpendicular to the radius PO → TO divides PQ into two segments of equal length: PQ=PR+RQ⇒8 =4+4 → In ∆PRO: RO²= PO²- PR² = 5²-4²=25-16=9 ⇒ RO=√ 9=3 → ∆PRO and ∆TPO are similar since their counterparts are perpendicular to each other → Ratio similarity = PO/R0 = 5/3 ⇒ TP=PR(5/3)=4x5/3=20/3

[pnachtwey]

OK, it is easy with nice numbers but what if thr numbers aren't nice ? What is the symbolic formula that will work for any nu bers?

[josevazdecarvalho]

This Result i can, t found but the value ca. 9, .24.

[shankarlalsaraswat]

बकवास। TP/PO=RP/RO कैसे हो जायेगा ? एक triangle TRP है। इसमें PO तो कोई arm है ही नहीं। ये इस तरह होगा ~
TP/PR= PO/ OR. इस तरह TP/ 4= 5/3= 20/3. किसी तरह उत्तर मिला दिया गया है। वीडियो बनाने से पहले हर point को देख लेना चाहिए। वैसे भी वीडियो ठीक से explain नहीं करता।