SATHEE: Properties of Triangles 1 Question 12

Properties of Triangles 1 Question 12

12. In a $△ P Q R, P$ is the largest angle and $\cos P = \frac{1}{3}$ . Further in circle of the triangle touches the sides $P Q, Q R$ and $R P$ at $N, L$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive even integers. Then, possible length(s) of the side(s) of the triangle is (are)

(2017 Main)

(a) 16

(b) 18

(d) 22

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Answer:

Correct Answer: 12. (b)

Solution:

PLAN Whenever cosine of angle and sides are given or to find out, we should always use Cosine law.

i.e. $\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$

and $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}$

$∴ \cos P = \frac{b^{2} + c^{2} - a^{2}}{2 b c}$

$\Rightarrow \frac{1}{3} = \frac{(2 n + 4)^{2} + (2 n + 2)^{2} - (2 n + 6)^{2}}{2 (2 n + 4) (2 n + 2)}$

$∵ \cos p = \frac{1}{3}$ , given

$\Rightarrow \frac{4 n^{2} - 16}{8 (n + 1) (n + 2)} = \frac{1}{3}$

$\Rightarrow \frac{n^{2} - 4}{2 (n + 1) (n + 2)} = \frac{1}{3}$

$\Rightarrow \frac{(n - 2)}{2 (n + 1)} = \frac{1}{3}$

$\Rightarrow 3 n - 6 = 2 n + 2 \Rightarrow n = 8$

$∴$ Sides are $(2 n + 2), (2 n + 4), (2 n + 6)$ , i.e. $18, 20, 22$ .

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Properties of Triangles 1 Question 12

Answer:

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Properties of Triangles 1 Question 12

12. In a △PQR,P is the largest angle and cos⁡P=13. Further in circle of the triangle touches the sides PQ,QR and RP at N,L and M respectively, such that the lengths of PN,QL and RM are consecutive even integers. Then, possible length(s) of the side(s) of the triangle is (are)

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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