Mathematics · JEE

Co-ordinate of the centroid, orthocentre and circumcentre of a triangle Mock Test for JEE

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Q1MathsUnit 10: Co-ordinate Geometry

P

is any point on the circumcircle of

\triangle A B C

other than the vertices.

H

is the orthocenter of

\triangle A B C, M

is the mid- point of

\boldsymbol{P H}

and

\boldsymbol{D}

is the mid-point of

B C .

Then

Q2MathsUnit 10: Co-ordinate Geometry

E

and

F

are the mid-point of sides

B C

CA and

A B

\triangle A B C,

then area

\triangle A B C

area

\triangle \mathrm{DEF}=

Q3MathsUnit 10: Co-ordinate Geometry

In an equilateral triangle

\Delta A B C

with sides

5 \mathrm{cm} .

Angle bisectors of

\angle A, \angle B, \angle C

meet at point

0 .

Measures of OA approximately is

Q4MathsUnit 10: Co-ordinate Geometry

Which condition of congruence will satisfy the diagram?

Q5MathsUnit 10: Co-ordinate Geometry

S

is the circumcentre,

O

is the orthocenter of

\triangle \boldsymbol{A B C}

, then

\boldsymbol{S A}+

\boldsymbol{S B}+\boldsymbol{S C}=

Q6MathsUnit 10: Co-ordinate Geometry

Let

\bar{a}, \bar{b}, \bar{c}

and

\bar{d}

be position vectors of four points

A, B, C

and

D

lying in a plane. If

(\bar{a}-\bar{d}) \cdot(\bar{b}-\bar{c})=0=

(\bar{b}-\bar{d}) \cdot(\bar{c}-\bar{a}),

then

\Delta A B C

has

D

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