If D, E, F are mid-points of the sides BC, CA and AB respectively of a triangle ABC, then which one of the following is not correctly matched?


A) If G is centroid of the \( \Large \triangle ABC \), then AG : GD = 2 : 1

B) If G is centroid of the \( \Large \triangle ABC \), then G is centroid of the \( \Large \triangle DEF \).

C) If \( \Large \ \angle A = 90 ^{\circ} \), then A is orthocentre of the \( \Large \triangle ABC \).

D) If \( \Large \ \angle A > 90 ^{\circ} \), then orthocentre of the \( \Large \triangle ABC \) lies inside the \( \Large \triangle ABC \).

Correct Answer:
C) If \( \Large \ \angle A = 90 ^{\circ} \), then A is orthocentre of the \( \Large \triangle ABC \).


Part of solved Triangle questions and answers : >> Elementary Mathematics >> Triangle








Comments

No comments available




Similar Questions
1). If lengths of two sides of a triangle are given, then its area is greater when
A). both the sides are greater than the third
B). angle between sides is a right angle.
C). angle between sides is an obtuse angle.
D). angle between sides is an acute angle.
-- View Answer
2). Consider following statements relating to the congruency of two right-angled triangles.
1. Equality of two sides of one triangle with same two sides of the second makes the triangle congruent.
2. Equality of hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangles congruent.
3. Equality of hypotenuse and an acute of triangle with the hypotenuse and an angle of the second respectively makes the triangles congruent.
Of these statements
A). 1, 2 and 3 are correct
B). 1 and 2 are correct
C). 1 and 3 are correct
D). 2 and 3 are correct
-- View Answer
3). If \( \Large \triangle ABC \) is a right angled triangle with \( \Large \angle A = 90 ^{\circ} \), AN is perpendicular to BC, BC =12cm and AC = 6cm, then the ratio of \( \Large \frac{area\ of \ \triangle ANC}{area\ of\ \triangle ABC} \) is
A). 1 : 2
B). 1 : 3
C). 1 : 4
D). 1 : 8
-- View Answer
4). In A PQR, the medians QM and RN intersect at O. PO meets QR in L. If OL is 2.5 cm, then PL is equal to
A). 5 cm
B). 10 cm
C). 2.5 cm
D). 7.5 cm
-- View Answer
5). If side of an equilateral triangle is \( \Large 20 \sqrt{3} cm \), then numerical value of the radius of the circle circumscribing the triangle is
A). 20 cm
B). \( \Large 20 \sqrt{3} cm \)
C). \( \Large 20 \pi cm \)
D). \( \Large \frac{20}{ \pi } cm \)
-- View Answer


6). To ensure that the two triangle ABC and DEF are congruent, the three conditions given below : AB=DE, AC=DF and \( \Large \angle ABC = \angle DEF \) are
A). sufficient but not necessary
B). necessary but not sufficient
C). neither necessary nor sufficient
D). both necessary as well as sufficient
-- View Answer
7). If D is a point on the side AB of \( \Large \triangle ABC \) and DE is a line through D meeting AC at E such that \( \Large \angle ADE = \angle ACB \), then AB AD is equal to
A). AE . BC
B). AC . DE
C). AE . AC
D). AB . BC
-- View Answer
8). D, E, F are mid points of BC, CA AB of \( \Large \triangle ABC \). If AD and BE intersect in G, then AG + BG + CG is equal to
A). AD = BE = CF
B). \( \Large \frac{2}{3} \) (AD+BE+CF)
C). \( \Large \frac{3}{2} \) (AD+BE+CF)
D). \( \Large \frac{1}{3} \) (AD+BE+CF)
-- View Answer
9). The square of the length of the tangent from \( \Large \left(3,\ -4\right) \) to the circle \( \Large x^{2}+y^{2}-4x-6y+3=0 \) is:
A). 20
B). 30
C). 40
D). 50
-- View Answer
10). If \( \Large g^{2}+f^{2}=c \) then the equation \( \Large x^{2}+y^{2}+2gx+2fy+c=0 \) will represent:
A). a Circle of radius g
B). a circle of radius f
C). a circle of diameter \( \Large \sqrt{c} \)
D). a circle of radius 0
-- View Answer