# Properties of Triangles · Mathematics · MHT CET

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MHT CET 2023 14th May Evening Shift
In a triangle $$\mathrm{A B C, m \angle A, m \angle B, m \angle C}$$ are in A.P. and lengths of two larger sides are 10 units, 9 units respectively, t...
MHT CET 2023 14th May Morning Shift
In $$\triangle \mathrm{ABC}$$, with usual notations, $$2 \mathrm{ac} \sin \left(\frac{1}{2}(\mathrm{~A}-\mathrm{B}+\mathrm{C})\right)$$ is equal to...
MHT CET 2023 14th May Morning Shift
If the angles $$\mathrm{A}, \mathrm{B}$$, and $$\mathrm{C}$$ of a triangle are in an Arithmetic Progression and if $$\mathrm{a}, \mathrm{b}$$ and $$\m... MHT CET 2023 13th May Evening Shift In$$\triangle A B C$$, with usual notations, if$$\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$$, then the value of$$\cos A+\cos B+\cos C$$is... MHT CET 2023 13th May Morning Shift The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides of the triangle (in unit... MHT CET 2023 13th May Morning Shift In$$\triangle A B C$$with usual notation,$$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$and$$a=\frac{1}{\sqrt{6}}$$, then the area of tria... MHT CET 2023 13th May Morning Shift Angles of a triangle are in the ratio$$4: 1: 1$$. Then the ratio of its greatest side to its perimeter is MHT CET 2023 12th May Evening Shift The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the length of the sides... MHT CET 2023 12th May Evening Shift If two angles of$$\triangle \mathrm{ABC}$$are$$\frac{\pi}{4}$$and$$\frac{\pi}{3}$$, then the ratio of the smallest and greatest sides are MHT CET 2023 12th May Evening Shift In$$\triangle \mathrm{ABC}, \mathrm{m} \angle \mathrm{B}=\frac{\pi}{3}$$and$$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{4}$$. Let point$$\mathrm{D}$$... MHT CET 2023 12th May Morning Shift In a triangle, the sum of lengths of two sides is$$x$$and the product of the lengths of the same two sides is$$y$$. If$$x^2-\mathrm{c}^2=y$$, wher... MHT CET 2023 11th May Evening Shift If the vertices of a triangle are$$(-2,3),(6,-1)$$and$$(4,3)$$, then the co-ordinates of the circumcentre of the triangle are MHT CET 2023 11th May Evening Shift In triangle$$\mathrm{ABC}$$with usual notations$$\mathrm{b}=\sqrt{3}, \mathrm{c}=1, \mathrm{~m} \angle \mathrm{A}=30^{\circ}$$, then the largest an... MHT CET 2023 11th May Evening Shift If the angles of a triangle are in the ratio$$4: 1: 1$$, then the ratio of the longest side to its perimeter is MHT CET 2023 11th May Morning Shift If in$$\triangle \mathrm{ABC}$$, with usual notations,$$a \cdot \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$$, then MHT CET 2023 11th May Morning Shift In a triangle$$\mathrm{ABC}$$, with usual notations, if$$\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathrm{a}=6$$and$$\mathrm{B}=\sin...
MHT CET 2023 10th May Evening Shift
In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{c}=4$$, then value of $$(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}$$ i...
MHT CET 2023 10th May Morning Shift
If one side of a triangle is double the other and the angles opposite to these sides differ by $$60^{\circ}$$, then the triangle is
MHT CET 2023 9th May Evening Shift
In $$\triangle \mathrm{PQR}, \sin \mathrm{P}, \sin \mathrm{Q}$$ and $$\sin \mathrm{R}$$ are in A.P., then
MHT CET 2023 9th May Evening Shift
Let $$a, b, c$$ be the lengths of sides of triangle $$A B C$$ such that $$\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}=k$$. Then $$\frac{(\mathrm{A}(\tri... MHT CET 2023 9th May Evening Shift In$$\triangle \mathrm{ABC}$$, with usual notations,$$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{2}$$, if$$\tan \left(\frac{A}{2}\right)$$and$$\tan \...
MHT CET 2023 9th May Morning Shift
Two sides of a triangle are $$\sqrt{3}+1$$ and $$\sqrt{3}-1$$ and the included angle is $$60^{\circ}$$, then the difference of the remaining angles is...
MHT CET 2021 24th September Evening Shift
In a triangle ABC with usual notations a = 2, b = 3, then value of $$\frac{\cos 2 \mathrm{~A}}{\mathrm{a}^2}-\frac{\cos 2 \mathrm{~B}}{\mathrm{~b}^2}... MHT CET 2021 24th September Morning Shift In any$$\triangle A B C$$, with usual notations,$$c(a \cos B-b \cos A)=$$MHT CET 2021 24th September Morning Shift If in a$$\triangle A B C$$, with usual notations,$$\mathrm{a}^2, \mathrm{~b}^2, \mathrm{c}^2$$are in A.P. then$$\frac{\sin 3 B}{\sin B}=$$MHT CET 2021 23rd September Evening Shift If$$\mathrm{G}(\overline{\mathrm{g}}), \mathrm{H}(\overline{\mathrm{h}})$$and$$\mathrm{P}(\overline{\mathrm{p}})$$are respectively centroid, ortho... MHT CET 2021 23rd September Evening Shift With usual notations in$$\triangle$$ABC, if$$\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}$$, then$$a^2, b^2, c^2$$are in MHT CET 2021 23rd September Evening Shift The area of the triangle$$\mathrm{ABC}$$is$$10 \sqrt{3} \mathrm{~cm}^2$$, angle$$\mathrm{B}$$is$$60^{\circ}$$and its perimeter is$$20 \mathrm{...
MHT CET 2021 23th September Morning Shift
In a triangle $$\mathrm{ABC}$$, with usual notations $$\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=5$$, then $$\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\c... MHT CET 2021 22th September Evening Shift In$$\Delta ABC$$, with usual notations$$\mathrm{\frac{b\sin B-c\sin C}{\sin(B-C)}}=$$MHT CET 2021 22th September Evening Shift With usual notations, in any$$\triangle A B C$$, if$$a\cos B=b \cos A$$, then the triangle is MHT CET 2021 22th September Morning Shift In$$\triangle A B C$$, with usual notations,$$2 a b \sin \frac{1}{2}(A+B-C)=$$MHT CET 2021 22th September Morning Shift If in$$\Delta$$ABC, with usual notations, the angles are in A.P., then$$\mathrm{\frac{a}{c}}$$sin 2 C +$$\mathrm{\frac{c}{a}}$$sin 2 A = MHT CET 2021 21th September Evening Shift With usual notations, perimeter of a triangle$$A B C$$is 6 times the arithmetic mean of sine of its angles. If$$\mathrm{a}=1$$, then measure of ang... MHT CET 2021 20th September Morning Shift With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio. MHT CET 2020 16th October Evening Shift In a$$\triangle A B C$$if$$2 \cos C=\sin B \cdot \operatorname{cosec} A$$, then MHT CET 2020 16th October Morning Shift In a triangle$$A B C$$with usual notations, if$$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$, then area of triangle$$A B C$$with$$a=\sqr...
MHT CET 2020 16th October Morning Shift
In a triangle $$A B C$$, if $$\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B$$, then $$A, B, C$$, are in
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