Question
Download Solution PDFकेंद्र O वाले एक वृत्त में, जीवाएँ PR और QS बढ़ाने पर बिंदु T पर मिलती हैं और PQ एक व्यास है। यदि
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
∠ROS = 42º
प्रयुक्त अवधारणा:
त्रिभुज के कोणों का योग = 180°
बाह्य कोण = सम्मुख अंतः कोणों का योग
केंद्र पर एक चाप द्वारा बनाया गया कोण = 2 × वृत्त की परिधि पर किसी भी बिंदु पर उसी चाप द्वारा बनाया गया कोण
गणना:
RQ और RS को मिलाइए
अवधारणा के अनुसार,
∠RQS = ∠ROS/2
⇒ ∠RQS = 42°/2 = 21° .....(1)
यहाँ, PQ एक व्यास है।
इसलिए, ∠PRQ = 90° [∵ अर्धवृत्त में कोण = 90°]
ΔRQT में, ∠PRQ एक बाह्यकोण है
इसलिए, ∠PRQ = ∠RTQ + ∠TQR
⇒ 90° = ∠RTQ + 21° [∵ ∠TQR = ∠RQS = 21°]
⇒ ∠RTQ = 90° - 21° = 69°
⇒ ∠PTQ = 69°
∴ ∠PTQ का माप 69° है।
Last updated on Jul 7, 2025
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