Question
Download Solution PDFदी गई आकृति में, ΔPQR में एक वृत्त इस प्रकार अंतर्गत है कि यह भुजाओं PQ, QR और RP को क्रमशः बिंदु D, E, F पर स्पर्श करता है। यदि भुजाओं की लंबाई PQ = 18 cm, QR = 13 cm और RP = 15 cm है, तो PD की लंबाई ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
PQ = 18 सेमी, QR = 13 सेमी और RP = 15 सेमी
प्रयुक्त अवधारणा:
किसी बाह्य बिंदु से वृत्त पर खींची गई स्पर्श रेखाओं की जोड़ी लंबाई में बराबर होती है।
अतः, PF = PD, DQ = EQ और FR = RE
गणना
मान लीजिए PD x सेमी है,
तो QD = (18 – x) सेमी
⇒ QE = (18 – x) cm
⇒ RE = 13 – (18 – x) = x – 5
⇒ RF = (x – 5)
⇒ PF = 15 – (x - 5) = 20 – x
⇒ 20 – x = x
⇒ 2x = 20
⇒ x = 20/2
⇒ x = 10 cm
⇒ PD = 10
उत्तर 10 है।
Last updated on Jul 17, 2025
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