Trắc nghiệm: Hệ thức lượng trong tam giác có đáp án

A. $\sqrt{19}$

B. $2\sqrt{19}$

C. $3\sqrt{19}$

D. $2\sqrt{7}$

A. 0,125

B. 0,25

C. 0,5

D. 0,0125

A. $\sqrt{2}$

B. $2\sqrt{2}$

C. 3

D. $\sqrt{10}$

A. ${m_a}^2+{m_b}^2+{m_c}^2=\frac{2}{3}\left(a^2+b^2+c^2\right)$

B. ${m_a}^2+{m_b}^2+{m_c}^2=\frac{4}{3}\left(a^2+b^2+c^2\right)$

C. ${m_a}^2+{m_b}^2+{m_c}^2=\frac{1}{3}\left(a^2+b^2+c^2\right)$

D. ${m_a}^2+{m_b}^2+{m_c}^2=\frac{3}{4}\left(a^2+b^2+c^2\right)$

A. $\frac{a\sqrt{3}}{3}$

B. $\frac{a\sqrt{3}}{2}$

C. $\frac{a\sqrt{3}}{4}$

D. $\frac{a\sqrt{2}}{2}$

A. 60

B. 30

C. $60\sqrt{3}$

D. $30\sqrt{3}$

A. 4

B. 3

C. 2

D. 1

A. $\frac{3}{4}$

B. $\frac{4}{3}$

C. $\frac{2}{3}$

D. $\frac{3}{2}$

A. $12\sqrt{6}$

B. $3\sqrt{6}$

C. $6\sqrt{6}$

D. $9\sqrt{6}$

A. $\frac{2\sqrt{14}}{7}$

B. $\frac{\sqrt{14}}{7}$

C. $\frac{4\sqrt{14}}{7}$

D. $\sqrt{14}$

A. 13

B. 26

C. 6,5

D. 7,5

A. 8

B. $4\sqrt{2}$

C. $2\sqrt{2}$

D. $2\sqrt{5}$

A. $\frac{1}{12}$

B. $-\frac{1}{12}$

C. $-\frac{1}{6}$

D. $\frac{1}{6}$

A. $135°$

B. $150°$

C. $60°$

D. $120°$

A. $135°$

B. $150°$

C. $60°$

D. $120°$

A. $135°$

B. $45°$

C. $120°$

D. $150°$

A. Tam giác nhọn

B. Tam giác tù

C. Tam giác vuông

D. Tam giác đều

A. Tam giác nhọn

B. Tam giác tù

C. Tam giác vuông

D. Tam giác đều

A. Tam giác nhọn

B. Tam giác tù

C. Tam giác vuông

D. Tam giác đều

A. $2\left(a^2+b^2+c^2\right)$

B. $a^2+b^2+c^2$

C. $\frac{a^2+b^2+c^2}{2}$

D. $\frac{a^2+b^2+c^2}{3}$

A. $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\frac{a^2+b^2+c^2}{abc}$

B. $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\frac{a^2+b^2+c^2}{2abc}$

C. $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\frac{a^2+b^2+c^2}{3abc}$

D. $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\frac{2\left(a^2+b^2+c^2\right)}{abc}$

A. $2\sqrt{23}$

B. $\sqrt{23}$

C. $\frac{\sqrt{23}}{2}$

D.5

A. $2\sqrt{10}$

B. $\sqrt{10}$

C. $3\sqrt{10}$

D. $\frac{\sqrt{10}}{2}$

A. $\frac{b^2+c^2-a^2}{3}$

B. $\frac{2b^2+2c^2-a^2}{4}$

C. $\frac{2b^2+2c^2-a^2}{12}$

D. $\frac{2b^2+2c^2-a^2}{9}$

A. Tam giác ABC là tam giác cân

B. Tam giác ABC là tam giác nhọn

C. Tam giác ABC là tam giác vuông

D.Tam giác ABC là tam giác tù

A. $R=10\sqrt{3}$

B. $R=20\sqrt{3}$

C. $R=10$

D. $R=20$

A. $30(cm{)}^2$

B. $15(cm{)}^2$

C. $60(cm{)}^2$

D. $7,5(cm{)}^2$

A. $3\sqrt{15}$

B. $6\sqrt{15}$

C. $\frac{3\sqrt{15}}{2}$

D. $\sqrt{15}$

A. 12

B. 6

C. $6\sqrt{3}$

D. $6\sqrt{2}$

A.1cm

B. 2 cm

C. 3 cm

D. 4 cm

A. $\sqrt{7}$

B. $\sqrt{3}$

C. $\sqrt{5}$

D.3

A. $7\sqrt{3}$

B. $\frac{7\sqrt{3}}{3}$

C. $\frac{7\sqrt{5}}{3}$

D. $\frac{7\sqrt{2}}{3}$

A. $12+8\sqrt{3}$

B. $24+16\sqrt{3}$

C. $24+4\sqrt{3}$

D. $24+8\sqrt{3}$

A. $96(cm{)}^2$

B. $16\sqrt{3}{\left(cm\right)}^2$

C. $96\sqrt{3}{\left(cm\right)}^2$

D. $48\sqrt{3}{\left(cm\right)}^2$

A. $\frac{1}{2}{a}^2\cos \alpha$

B. $\frac{1}{2}{a}^2\sin \alpha$

C. $a^2\cos \alpha$

D. $a^2\sin \alpha$

A. $\frac{1}{2}n{R}^2\sin {\left(\frac{360}{n}\right)}^{°}$

B. $\frac{1}{2}n{R}^2\cos {\left(\frac{360}{n}\right)}^{°}$

C. $n{R}^2\sin {\left(\frac{360}{n}\right)}^{°}$

D. $n{R}^2\text{cos}{\left(\frac{360}{n}\right)}^{°}$

A. $48(cm{)}^2$

B. $32(cm{)}^2$

C. $40{\left(cm\right)}^2$

D. $56{\left(cm\right)}^2$

A.13/2

B. $\frac{13\sqrt{3}}{2}$

C.13

D. $13\sqrt{3}$

A. $\hat{A}=30$

B. $\hat{A}=150$

C. $\hat{A}=90$

D. $\hat{A}=30°họăc\hat{A}=150$

A. $(R.\cos A)/a$

B. $(R.\cos A)/2a$

C. $(2R.\cos A)/a$

D. $(2R.\sin A)/a$

A. $\frac{R.\left(b^2+c^2-a^2\right)}{abc}$

B. $\frac{R.\left(b^2+c^2-a^2\right)}{2abc}$

C. $\frac{2R.\left(b^2+c^2-a^2\right)}{abc}$

D. $\frac{R.\left(b^2+c^2-a^2\right)}{4abc}$

A. $\cot A+\cot B+\cot C=\frac{a^2+b^2+c^2}{2S}$

B. $\cot A+\cot B+\cot C=\frac{a^2+b^2+c^2}{4S}$

C. $\cot A+\cot B+\cot C=\frac{a^2+b^2+c^2}{S}$

D. $\cot A+\cot B+\cot C=\frac{2\left(a^2+b^2+c^2\right)}{S}$

A. $h_b=2h_a$

B. $h_b=h_a$

C. $h_a=2h_b$

D. $h_b=4h_a$

A. sin B + sin C = 2 sin A

B. sin C + sin A = 2 sin B

C. sin A + sin B = 2 sin C

D. sin A + sin B = sin C

A. $\sin A\sin B=si{n}^{2}C$

B. $\sin A\sin B=2si{n}^{2}C$

C. $\sin A\sin B=4si{n}^{2}C$

D. $2\sin A\sin B=si{n}^{2}C$

A. sinB + sinC > sinA

B. sinC + sinA > sinB

C. sinA + sinB > sinC

D. $\sin A+\sin B\le \sin C$

A. R sinα

B. $2Rcos\frac{\alpha }{2}$

C. $R\cos \alpha /2$

D. 2R sinα

A. $\frac{r}{h_a}=\frac{2a}{4a+b+c}$

B. $\frac{r}{h_a}=\frac{a}{a+b+c}$

C. $\frac{r}{h_a}=\frac{a}{-a+2b+2c}$

D. $\frac{r}{h_a}=\frac{2a}{a+b+c}$

A. $\frac{1}{2}{R}^2\left(\sin 2A+\sin 2B+\sin 2C\right)$

B. $\frac{1}{2}{R}^2\left(\sin A+\sin B+\sin C\right)$

C. $R^2\left(\sin 2A+\sin 2B+\sin 2C\right)$

D. $R^2\left(\sin A+\sin B+\sin C\right)$

A. $\frac{S_{AMN}}{S_{ABC}}=3\frac{AM}{AB}.\frac{AN}{AC}$

B. $\frac{S_{AMN}}{S_{ABC}}=\frac{1}{2}\frac{AM}{AB}.\frac{AN}{AC}$

C. $\frac{S_{AMN}}{S_{ABC}}=2\frac{AM}{AB}.\frac{AN}{AC}$

D. $\frac{S_{AMN}}{S_{ABC}}=\frac{AM}{AB}.\frac{AN}{AC}$

A. $2\left(a^2+b^2+c^2\right)$

B. $a^2+b^2+c^2$

C. $\frac{a^2+b^2+c^2}{2}$

D. $\frac{a^2+b^2+c^2}{3}$

A. $2\sqrt{23}$

B. $\sqrt{23}$

C. $\frac{\sqrt{23}}{2}$

D.5

A. $2\sqrt{10}$

B. $\sqrt{10}$

C. $3\sqrt{10}$

D. $\frac{\sqrt{10}}{2}$

A. $\frac{b^2+c^2-a^2}{3}$

B. $\frac{2b^2+2c^2-a^2}{4}$

C. $\frac{2b^2+2c^2-a^2}{12}$

D. $\frac{2b^2+2c^2-a^2}{9}$

A. Tam giác ABC là tam giác cân

B. Tam giác ABC là tam giác nhọn

C. Tam giác ABC là tam giác vuông

D.Tam giác ABC là tam giác tù

A. $R=10\sqrt{3}$

B. $R=20\sqrt{3}$

C. $R=10$

D. $R=20$

A. $30(cm{)}^2$

B. $15(cm{)}^2$

C. $60(cm{)}^2$

D. $7,5(cm{)}^2$

A. $3\sqrt{15}$

B. $6\sqrt{15}$

C. $\frac{3\sqrt{15}}{2}$

D. $\sqrt{15}$

A. 12

B. 6

C. $6\sqrt{3}$

D. $6\sqrt{2}$

A.1cm

B. 2 cm

C. 3 cm

D. 4 cm

A. $\sqrt{7}$

B. $\sqrt{3}$

C. $\sqrt{5}$

D.3

A. $7\sqrt{3}$

B. $\frac{7\sqrt{3}}{3}$

C. $\frac{7\sqrt{5}}{3}$

D. $\frac{7\sqrt{2}}{3}$

A. $12+8\sqrt{3}$

B. $24+16\sqrt{3}$

C. $24+4\sqrt{3}$

D. $24+8\sqrt{3}$

A. $96(cm{)}^2$

B. $16\sqrt{3}{\left(cm\right)}^2$

C. $96\sqrt{3}{\left(cm\right)}^2$

D. $48\sqrt{3}{\left(cm\right)}^2$

A. $\frac{1}{2}{a}^2\cos \alpha$

B. $\frac{1}{2}{a}^2\sin \alpha$

C. $a^2\cos \alpha$

D. $a^2\sin \alpha$

A. $\frac{1}{2}n{R}^2\sin {\left(\frac{360}{n}\right)}^{°}$

B. $\frac{1}{2}n{R}^2\cos {\left(\frac{360}{n}\right)}^{°}$

C. $n{R}^2\sin {\left(\frac{360}{n}\right)}^{°}$

D. $n{R}^2\text{cos}{\left(\frac{360}{n}\right)}^{°}$

A. $48(cm{)}^2$

B. $32(cm{)}^2$

C. $40{\left(cm\right)}^2$

D. $56{\left(cm\right)}^2$

A.13/2

B. $\frac{13\sqrt{3}}{2}$

C.13

D. $13\sqrt{3}$

A. $\hat{A}=30$

B. $\hat{A}=150$

C. $\hat{A}=90$

D. $\hat{A}=30°họăc\hat{A}=150$

A. $(R.\cos A)/a$

B. $(R.\cos A)/2a$

C. $(2R.\cos A)/a$

D. $(2R.\sin A)/a$

A. $\frac{R.\left(b^2+c^2-a^2\right)}{abc}$

B. $\frac{R.\left(b^2+c^2-a^2\right)}{2abc}$

C. $\frac{2R.\left(b^2+c^2-a^2\right)}{abc}$

D. $\frac{R.\left(b^2+c^2-a^2\right)}{4abc}$

A. $\cot A+\cot B+\cot C=\frac{a^2+b^2+c^2}{2S}$

B. $\cot A+\cot B+\cot C=\frac{a^2+b^2+c^2}{4S}$

C. $\cot A+\cot B+\cot C=\frac{a^2+b^2+c^2}{S}$

D. $\cot A+\cot B+\cot C=\frac{2\left(a^2+b^2+c^2\right)}{S}$

A. $h_b=2h_a$

B. $h_b=h_a$

C. $h_a=2h_b$

D. $h_b=4h_a$

A. sin B + sin C = 2 sin A

B. sin C + sin A = 2 sin B

C. sin A + sin B = 2 sin C

D. sin A + sin B = sin C

A. $\sin A\sin B=si{n}^{2}C$

B. $\sin A\sin B=2si{n}^{2}C$

C. $\sin A\sin B=4si{n}^{2}C$

D. $2\sin A\sin B=si{n}^{2}C$

A. sinB + sinC > sinA

B. sinC + sinA > sinB

C. sinA + sinB > sinC

D. $\sin A+\sin B\le \sin C$

A. R sinα

B. $2Rcos\frac{\alpha }{2}$

C. $R\cos \alpha /2$

D. 2R sinα

A. $\frac{r}{h_a}=\frac{2a}{4a+b+c}$

B. $\frac{r}{h_a}=\frac{a}{a+b+c}$

C. $\frac{r}{h_a}=\frac{a}{-a+2b+2c}$

D. $\frac{r}{h_a}=\frac{2a}{a+b+c}$

A. $\frac{1}{2}{R}^2\left(\sin 2A+\sin 2B+\sin 2C\right)$

B. $\frac{1}{2}{R}^2\left(\sin A+\sin B+\sin C\right)$

C. $R^2\left(\sin 2A+\sin 2B+\sin 2C\right)$

D. $R^2\left(\sin A+\sin B+\sin C\right)$

A. $\frac{S_{AMN}}{S_{ABC}}=3\frac{AM}{AB}.\frac{AN}{AC}$

B. $\frac{S_{AMN}}{S_{ABC}}=\frac{1}{2}\frac{AM}{AB}.\frac{AN}{AC}$

C. $\frac{S_{AMN}}{S_{ABC}}=2\frac{AM}{AB}.\frac{AN}{AC}$

D. $\frac{S_{AMN}}{S_{ABC}}=\frac{AM}{AB}.\frac{AN}{AC}$