SSC CGL 201921)△ABC and △DBC are on the same BC but on opposite sides of it. AD and BC intersect each other at O.If AO = a cm, DO = b cm and the area of △ABC = x cm sq, then what is the area(in cm sq.) of △DBC ?

Correct Option: C

\({bx\over a}\)

SSC CGL 201922)In \(\triangle ABC\), the perpendiculars drawn from A, B and C meet the opposite sides at D, E and F, respectively. AD, BE and CF intersect at point P. If \(\angle EPD=116^0\) and the bisectors of \(\angle A\) and \(\angle B\) meet at Q, then the measure of is \(\angle AQB\) is :

Correct Option: B

\(122^0\)

SSC CGL 201923)The perimeters of two similar triangles ABC and PQR are 78 cm and 46.8 cm, respectively. If PQ = 11.7 cm., then the length of AB is:

Correct Option: A

19.5 cm.

SSC CGL 201924)In \(\triangle PQR\), I is the incentre of the triangle. If \(\angle QIR=107^0\), then what is the measure of \(\angle P\)?

Correct Option: D

\(34^0\)

SSC CGL 201925)The sides PQ and PR of \(\triangle PQR\) are produced to points S and T, respectively. The bisectors of \(\angle SQR\) and \(\angle TRQ\)meet at U. If \(\angle QUR=79^0\), then the measure of \(\angle P\) is:

Correct Option: C

\(22^0\)

SSC CGL 201926)In \(\triangle ABC\), AB = AC and D is a point on BC. If BD = 5 cm, AB = 12 cm and AD = 8 cm, then the length of CD is:

Correct Option: C

16 cm

SSC CGL 201927)The bisector of \(\angle B\) in \(\triangle ABC\) meets AC at D. If AB = 10 cm, BC = 11 cm and AC = 14 cm, then the length of AD is:

Correct Option: D

\(20\over3\) cm

SSC CGL 202028)Arrange the angles of the triangle from smallest to largest in the triangle, where the sides are AB = 7 cm, AC = 8 cm, and BC = 9 cm.

Correct Option: C

C,B,A

Measurement of angle is according to the length of opposite line.

So, The order of the angles of the triangle from smallest to largest in the triangle,

C < B < A.

SSC CGL 202029)In the triangle, If AB = AC and \(\angle ABC = 72^0\), then \(\angle BAC\) is:

Correct Option: A

\(36^0\)

By triangle properties,

When AB = AC then \(\angle ABC = \angle ACB\) so,

In\(\triangle ABC,\)

\(\Rightarrow \angle ABC + \angle ACB + \angle BAC = 180^{0}\);

\(\Rightarrow \angle ABC + \angle ABC + \angle BAC = 180^{0}\);

\(\Rightarrow 72^{0} + 72^{0} + \angle BAC = 180^{0}\);

\(\Rightarrow \angle BAC = 180^{0} - 144^{0} = 36^{0}\)

30)In the given figure, a circle inscribed in triangle PQR touches its sides PQ, QR and RP at points S, T and U,respectively. If PQ = 15 cm, QR= 10 cm, and RP = 12 cm, then find the lengths of PS, QT and RU?

SSC CGL 2020

Correct Option: D

PS = 8.5 cm, QT = 6.5 cm and RU = 3.5 cm

PQ = 15 cm, QR= 10 cm, and RP = 12 cm. ;

PQ = x + y = 15------------------(i);

QR = y + z = 10----------(ii);

RP = z + x = 12 ------(iii);

Solving equation, we get :

z = 3.5 cm = RU;

y = 6.5 cm = QT;

x = 8.5 cm = PS

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