Q.1
PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is:
Q.2
In ΔABC, ∠BAC = 90° and AD ⊥ BC. If BD = 3 cm and CD = 4 cm, then length of AD is :
Q.3
ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12$$\sqrt 5 $$ and BC = 24 cm then radius of circle is:
Q.4
Let ABC be an equilateral triangle and AD perpendicular to BC, then AB2 + BC2 + CA2 = ?
Q.5
Incenter of ΔABC is I. ∠ABC = 90° and ∠ACB = 70°. ∠BIC is:
Q.6
If in ΔABC, DE || BC, AB = 7.5 cm BD = 6 cm and DE = 2 cm then the length of BC in cm is:
Q.7
In a ΔPQR, ∠Q = 55° and ∠R = 35°. Find the ratio of angles subtended by side QR on circumcenter, incenter and orthocenter of the triangle.
Q.8
In ΔPQR, straight line parallel to the base QR cuts PQ at X and PR at Y. If PX : XQ = 5 : 6, then XY : QR will be
Q.9
In ΔABC, ∠B = 60° and ∠C = 40°; AD and AE are respectively the bisector of ∠A and perpendicular on BC. The measure of ∠EAD is:
Q.10
ABC is a triangle in which ∠A = 90°. Let P be any point on side AC. If BC = 10 cm, AC = 8 cm and BP = 9 cm, then AP = ?
Q.11
In ΔABC, the line parallel to BC intersect AB & AC at P & Q respectively. If AB : AP = 5 : 3, then AQ : QC is:
Q.12
∠A of ΔABC is a right angle. AD is perpendicular on BC. If BC = 14 and BD = 5 cm, then measure of AD is:
Q.13
In ΔABC, if AD ⊥ BC, then AB2 + CD2 is equal to
Q.14
In ΔABC, the external bisectors of the angles ∠B and ∠C meet at the point O. If ∠A = 70°, then the measure of ∠BOC is :
Q.15
If I be the incentre of ΔABC and ∠B = 70° and ∠C = 50°, then the magnitude of ∠BIC is
Q.16
In ΔABC, AD ⊥ BC and AD2 = BD × DC. The measure of ∠BAC is :
Q.17
For a triangle ABC, D, E, F are the mid - point of its sides. If ΔABC = 24 sq. units then ΔDEF is :
Q.18
If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, ∠BGC = 60°, BC = 8 cm, then area of the triangle ABC is:
Q.19
In ΔABC, AB = BC = K, AC = $$\sqrt 2 $$ k, then ΔABC is a :
Q.20
If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19 cm and AC = 22 cm then the length of BC is :
Q.21
The sum of three altitudes of a triangle is
Q.22
In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e., hypotenuse. One of the acute angle must be
Q.23
In ΔABC, ∠B = 60° and ∠C = 40°. If AD and AE be respectively the internal bisector of ∠A and perpendicular on BC, then the measure of ∠DAE is
Q.24
If the measures of the sides of triangle are (x2 - 1), (x2 + 1) and 2x cm, then the triangle would be :
Q.25
In ΔABC, ∠C is an obtuse angle. The bisectors of the exterior angles at A and B meet BC and AC produced at D and E respectively. If AB = AD = BE, then ∠ACB = ?
Q.26
In ΔABC, DE || AC, D and E are two points on AB and CB respectively. If AB = 10 cm and AD = 4 cm, then BE : CE is
Q.27
Let ABC be an equilateral triangle and AX, BY, CZ be the altitude. Then the right statement out of the four give responses is :
Q.28
An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75° = ?
Q.29
If the sides of a right angled triangle are three consecutive integers, then the length of the smallest side is
Q.30
In a triangle ABC, the side BC is extended up to D such that CD = AC. If ∠BAD = 109° and ∠ACB = 72° then the value of ∠ABC is
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