Question
Download Solution PDFदी गई आकृति में, Δ PQR में एक वृत्त इस प्रकार बनाया गया है कि यह भुजाओं PQ, QR और RP को क्रमशः बिंदु D, E, F पर स्पर्श करता है। यदि भुजाओं की लम्बाई PQ = 15 सेमी, QR = 11 सेमी और RP = 13 सेमी है, तो PD की लम्बाई ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
Δ PQR में,
PQ = 15 सेमी, QR = 11 सेमी और RP = 13 सेमी
Δ PQR में एक वृत्त इस प्रकार बनाया गया है कि यह भुजाओं PQ, QR और RP को क्रमशः बिंदु D, E, F पर स्पर्श करता है।
प्रयुक्त सूत्र:
एक बिंदु से वृत्त पर खींची गई स्पर्श रेखाएँ लम्बाई में बराबर होती हैं।
गणना:
Δ PQR में एक वृत्त इस प्रकार बनाया गया है कि यह भुजाओं PQ, QR और RP को क्रमशः बिंदु D, E, F पर स्पर्श करता है।
⇒ PD = PF = x
⇒ QD = QE = y
⇒ RE = RF = z
सभी स्पर्शरेखाएँ हैं।
⇒ PD + PF + QD + QE + RE + RF = PQ + QR + RP
⇒ x + x + y + y + z + z = 39
⇒ 2x + 2(y + z) = 39
यहाँ,
y + z = QE + ER = RQ
और हमारे पास, RQ = 11 है,
⇒ 2x + 2(11) = 39
⇒ 2x + 22 = 39
⇒ 2x = 17
⇒ x = 8.5
⇒ PD = 8.5 सेमी
∴ सही उत्तर विकल्प 4 है।
Last updated on Jul 21, 2025
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