The vertices of - ABC are A4-6-B1-5 and C7-2-Find the circumcenter of - ABC-

A(4,6);B(1,5);C(7,2) The circumcenter of the triangle is given by #160; (x_1+x_2+x_33,y_1+y_2+y_33) (4+1+73,6+5+23) (123,133)=(4,133) ...

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Byju's Answer

Standard VII

Mathematics

Area of a Triangle

The vertices ...

Question

The vertices of $Δ A B C$ are $A (4, 6), B (1, 5)$ and $C (7, 2)$ .Find the circumcenter of $Δ A B C$ .

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Solution

$A (4, 6); B (1, 5); C (7, 2)$

The circumcenter of the triangle is given by

$(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$
$(\frac{4 + 1 + 7}{3}, \frac{6 + 5 + 2}{3})$

$(\frac{12}{3}, \frac{13}{3}) = (4, \frac{13}{3})$

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Similar questions

The vertices of a $Δ$ ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB at D, such that AD/AB= $\frac{1}{4}$ . Calculate the area of the $Δ$ ADC.

Q. In fig. 8, the vertices of

Δ A B C

are

A (4, 6), B (1, 5)

and

C (7, 2)

. A line-segment DE is drawn to intersect the sides AB and AC at D and E respectively such that

\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{3}

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and compare it with area of

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Q. The vertices of a

Δ A B C

are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides AB and AC at D and E respectively, such that

\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{4}

. Calculate the area of the

Δ A D E

and compare it with the area of

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. (Recall Theorem 6.2 and Theorem 6.6).

The vertices of a ΔABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that. Calculate the area of the ΔADE and compare it with the area of ΔABC. (Recall Converse of basic proportionality theorem and Theorem 6.6 related to

ratio of areas of two similar triangles)

The vertices of a $Δ A B C$ are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that
$\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{4}$ . Calculate the ratio of the area of the $Δ A D E$ and $Δ A B C$ .

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The vertices of ΔABC are A(4,6),B(1,5) and C(7,2).Find the circumcenter of ΔABC.

A(4,6);B(1,5);C(7,2)The circumcenter of the triangle is given by (x1+x2+x33,y1+y2+y33)(4+1+73,6+5+23)(123,133)=(4,133)

The vertices of $Δ A B C$ are $A (4, 6), B (1, 5)$ and $C (7, 2)$ .Find the circumcenter of $Δ A B C$ .

$A (4, 6); B (1, 5); C (7, 2)$

The circumcenter of the triangle is given by

$(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$
$(\frac{4 + 1 + 7}{3}, \frac{6 + 5 + 2}{3})$

$(\frac{12}{3}, \frac{13}{3}) = (4, \frac{13}{3})$