## Properties of Triangle

### Mathematics

#### (Past Years Questions)

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A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter tha...
JEE Main 2021 (Online) 31st August Morning Shift
Two poles, AB of length a metres and CD of length a + b (b $$\ne$$ a) metres are erected at the same horizontal level wi...
JEE Main 2021 (Online) 27th August Evening Shift
Let $${{\sin A} \over {\sin B}} = {{\sin (A - C)} \over {\sin (C - B)}}$$, where A, B, C are angles of triangle ABC. If ...
JEE Main 2021 (Online) 27th August Morning Shift
A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that P...
JEE Main 2021 (Online) 26th August Evening Shift
A spherical gas balloon of radius 16 meter subtends an angle 60$$^\circ$$ at the eye of the observer A while the angle o...
JEE Main 2021 (Online) 25th July Morning Shift
Let in a right angled triangle, the smallest angle be $$\theta$$. If a triangle formed by taking the reciprocal of its s...
JEE Main 2021 (Online) 20th July Evening Shift
If in a triangle ABC, AB = 5 units, $$\angle B = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$ and radius of circumcircle...
JEE Main 2021 (Online) 20th July Morning Shift
A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corne...
JEE Main 2021 (Online) 18th March Evening Shift
The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :
JEE Main 2021 (Online) 26th February Evening Shift
A man is observing, from the top of a tower, a boat speeding towards the lower from a certain point A, with uniform spee...
JEE Main 2021 (Online) 25th February Morning Slot
The angle of elevation of a jet plane from a point A on the ground is 60$$^\circ$$. After a flight of 20 seconds at the ...
JEE Main 2021 (Online) 24th February Evening Slot
Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of t...
JEE Main 2021 (Online) 24th February Morning Slot
The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards t...
JEE Main 2020 (Online) 6th September Evening Slot
The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the i...
JEE Main 2020 (Online) 4th September Evening Slot
A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If $$\angle BAC = {90^o}$$ and area$... JEE Main 2020 (Online) 4th September Morning Slot The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45o from a point ... JEE Main 2019 (Online) 12th April Evening Slot The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : $$\sqrt 3$$. If c = 4 cm, then the area (in sq. cm)... JEE Main 2019 (Online) 10th April Evening Slot ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles o... JEE Main 2019 (Online) 10th April Morning Slot Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an ... JEE Main 2019 (Online) 9th April Evening Slot Two vertical poles of heights, 20 m and 80 m stand a part on a horizontal plane. The height (in meters) of the point of ... JEE Main 2019 (Online) 8th April Evening Slot If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of len... JEE Main 2019 (Online) 8th April Evening Slot If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30o and the angle of depression of ref... JEE Main 2019 (Online) 12th January Evening Slot Given $${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$ for a $$\Delta$$ABC with usual notation. ... JEE Main 2019 (Online) 11th January Evening Slot 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 x2 – c... JEE Main 2019 (Online) 11th January Morning Slot With the usual notation, in $$\Delta$$ABC, if $$\angle A + \angle B$$ = 120o, a = $$\sqrt 3$$ $$+$$ 1, b = $$\sqrt 3... JEE Main 2019 (Online) 10th January Evening Slot Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC su... JEE Main 2019 (Online) 10th January Morning Slot A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If... JEE Main 2018 (Online) 16th April Morning Slot A tower T1 of height 60 m is located exactly opposite to a tower T2 of height 80 m on a straight road. Fromthe top of T1... JEE Main 2018 (Online) 15th April Evening Slot An aeroplane flying at a constant speed, parallel to the horizontal ground,$$\sqrt 3 $$kmabove it, is obsered at an el... JEE Main 2018 (Online) 15th April Morning Slot The angle of elevation of the top of a vertical tower from a point A, due east of it is 45o. The angle of elevation of t... JEE Main 2016 (Online) 10th April Morning Slot If the angles of elevation of the top of a tower from three collinear points$$A, B$$and$$C,$$on a line leading to th... JEE Main 2015 (Offline) A bird is sitting on the top of a vertical pole$$20$$m high and its elevation from a point$$O$$on the ground is$${4... JEE Main 2014 (Offline) For a regular polygon, let $$r$$ and $$R$$ be the radii of the inscribed and the circumscribed circles. A $$false$$ stat... AIEEE 2010 $$AB$$ is a vertical pole with $$B$$ at the ground level and $$A$$ at the top. $$A$$ man finds that the angle of elevati... AIEEE 2008 A tower stands at the centre of a circular park. $$A$$ and $$B$$ are two points on the boundary of the park such that $$... AIEEE 2007 In a triangle$$ABC$$, let$$\angle C = {\pi \over 2}$$. If$$r$$is the inradius and$$R$$is the circumradius of the ... AIEEE 2005 If in a$$\Delta ABC$$, the altitudes from the vertices$$A, B, C$$on opposite sides are in H.P, then$$\sin A,\sin B,\... AIEEE 2005 The sides of a triangle are $$\sin \alpha ,\,\cos \alpha$$ and $$\sqrt {1 + \sin \alpha \cos \alpha }$$ for some $$0 &... AIEEE 2004 A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank ... AIEEE 2004 If in a$$\Delta ABCa{\cos ^2}\left( {{C \over 2}} \right) + {\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2}... AIEEE 2003 In a triangle $$ABC$$, medians $$AD$$ and $$BE$$ are drawn. If $$AD=4$$, $$\angle DAB = {\pi \over 6}$$ and $$\angle A... AIEEE 2003 The sum of the radii of inscribed and circumscribed circles for an$$n$$sided regular polygon of side$$a, $$is AIEEE 2003 In a triangle with sides$$a, b, c,{r_1} &gt; {r_2} &gt; {r_3}$$(which are the ex-radii) then AIEEE 2002 The sides of a triangle are$$3x + 4y,4x + 3y$$and$$5x + 5y$$where$$x$$,$$y&gt;0$$then the triangle is AIEEE 2002 ## Numerical More If a rectangle is inscribed in an equilateral triangle of side length$$2\sqrt 2 $$as shown in the figure, then the squ... JEE Main 2021 (Online) 25th July Evening Shift In$$\Delta$$ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of$$\Delta$\$ABC is 30 cm...
JEE Main 2021 (Online) 16th March Evening Shift
Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius is drawn. Another circle C2 ...
JEE Main 2021 (Online) 16th March Morning Shift
The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is...
JEE Main 2020 (Online) 6th September Morning Slot