\(\Delta\)ABC में, \(\overline {AD}\)\(\angle\)A को समद्विविभाजित करता है और D, \(\overline {BC}\) पर एक बिंदु है।  यदि m (\(\overline {AC}\)) = 4.2 सेमी, m (\(\overline {BD}\)) = 4 सेमी और m (\(\overline {BC}\)) = 7 सेमी है, तो m (\(\overline {AB}\)) ज्ञात कीजिए। 

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RRB Group D 6 Oct 2022 Shift 1 Official Paper
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  1. 5.2 सेमी
  2. 4.2 सेमी
  3. 4.8 सेमी
  4. 5.6 सेमी

Answer (Detailed Solution Below)

Option 4 : 5.6 सेमी
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दिया है:

\(\Delta\)ABC में, \(\overline {AD}\) \(\angle\)A को समद्विविभजित करता है और D  \(\overline {BC}\) पर एक बिंदु है।  यदि m (\(\overline {AC}\)) = 4.2 सेमी, m (\(\overline {BD}\)) = 4 सेमी और m (\(\overline {BC}\)) = 7 सेमी है। 

गणना:

DC = BC - BD = 7 - 4 = 3 सेमी 

कोण द्विभाजक प्रमेय के अनुसार:

AB : AC = BD : DC

⇒ AB : 4.2 = 4 : 3

⇒ AB = 4 × 4.2/3

⇒ AB = 5.6 cm

अतः अभीष्ट मान 5.6 सेमी है।

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