AP EAMCET · Maths · Properties of Triangles
In \(\triangle \mathrm{ABC}\), if \(b=2, c=\sqrt{3},\left\lfloor\mathrm{~A}=30^{\circ}\right.\), then its inradius \(r=\)
- A \(\sqrt{3}-1\)
- B \(\sqrt{3}+1\)
- C \(\frac{\sqrt{3}+1}{2}\)
- D \(\frac{\sqrt{3}-1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sqrt{3}-1}{2}\)
Step-by-step Solution
Detailed explanation
\(a^2 = b^2 + c^2 - 2bc \cos A = 2^2 + (\sqrt{3})^2 - 2(2)(\sqrt{3}) \cos 30^{\circ} = 4+3-6 = 1\) \(a = 1\) \(K = \frac{1}{2}bc \sin A = \frac{1}{2}(2)(\sqrt{3}) \sin 30^{\circ} = \frac{\sqrt{3}}{2}\) \(s = \frac{a+b+c}{2} = \frac{1+2+\sqrt{3}}{2} = \frac{3+\sqrt{3}}{2}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The range of a random variable \(X\) is \(\{0,1,2\}\). If \(P(X=0)\) \(=3 \mathrm{C}^3, \mathrm{P}(\mathrm{X}=1)=4 \mathrm{C}-10 \mathrm{C}^2\) and \(\mathrm{P}(\mathrm{X}=2)=5 \mathrm{C}-1\), then the value of \(\mathrm{C}\) isAP EAMCET 2023 Medium
- Let \(\overline{O A}=-4 \bar{i}+3 \bar{k}, \overline{O B}=14 \bar{i}+2 \bar{j}-5 \bar{k} \cdot \overline{O D}\) bisects \(\angle A O B\) and \(|\overline{O D}|=\sqrt{6}\), then \(\overline{O D}=\)AP EAMCET 2022 Easy
- A line \(l\) meets the circle \(x^2+y^2=61\) in \(A, B\) and \(P(-5,6)\) is such that \(P A=P B=10\). Then, the equation of \(l\) isAP EAMCET 2004 Easy
- Let \(f(x)=\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}\). If \(\lim _{x \rightarrow m} f(x)=5 / 2\), then set of all possible finite values of 1 and \(m\) isAP EAMCET 2023 Easy
- A box contains 30 toys of same size in which 10 toys are white and all the remaining toys are blue. A toy is drawn at random from the box and it is replaced in the box after noting down its colour. If 5 toys are drawn in this way, then the probability of getting atmost 2 white toys isAP EAMCET 2019 Hard
- \(\tan \left(-\frac{23 \pi}{3}\right)-\cot \left(\theta-\frac{13 \pi}{3}\right)=\)AP EAMCET 2020 Medium
More PYQs from AP EAMCET
- To which orbital among the following may an electron having zero angular momentum belong?AP EAMCET 2021 Easy
- A particle starting from mean position executes simple harmonic motion with a period \(8 \mathrm{~s}\). The minimum time in which its potential energy becomes half of the total energy is __________ .AP EAMCET 2017 Easy
- If the lengths of the tangents drawn from a point to the three circles and are equal, then the coordinates of areAP EAMCET 2018 Medium
- The order of basic strength of the following in aqueous solution is
I. \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2\)
II. \(\left(\mathrm{CH}_3\right)_3 \mathrm{~N}\)
III. \(\mathrm{NH}_3\)
IV. \(\mathrm{CH}_3 \mathrm{NH}_2\)
V. \(\left(\mathrm{CH}_3\right)_2 \mathrm{NH}\)AP EAMCET 2016 Easy - If \(x=2 \cos ^3 \theta\) and \(y=3 \sin ^2 \theta\), then \(\frac{d y}{d x}=\)AP EAMCET 2025 Medium
- The area (in sq. units) enclosed between the curves \(y=x^2\) and \(y=|x|\) isAP EAMCET 2017 Easy