Question

7. In theright angled triangleABC, angle B=90°, A=
(2,5,1), B = (1,4,-3) and C=(-2, 7,-3). If P,
S, R are the orthocentre, circumcentre,
circumradius of the triangle ABC then R+ Py =
(1) 7 2 )10 3)8 4) 13​

Answer 1

answer is 7

please mark it as the brainliest...plzzz

Answer 2

Answer:

Step-by-step explanation:

Concept:

The concept of triangle in geometry  will be used to solve this equation.

Given:

The triangle is $ABC$, Angle $B= 90^\circ$  and $A=(2,5,1), B = (1,4,-3)$ and $C=(-2, 7,-3)$

The orthocentre is $P$ , circumcentre is $S$ and circumradius of the triangle is $R$ .

To Find:

The equation is $R+P_{y}$  is given to solve.

Solution:

In a right angle triangle the vertex of the right angle is the orthocentre.

Here $B$ is the orthocentre.

Therefore we can say $B=P$ .

So that we can write $P_y}$ is $4$ as we know $P=(1,4,-3)$

Here $R$ is circumcentre .

Then length of $R$ is $\frac{1}{2} \times AC$

First we have to solve the value of $AC$

According to the image, we can write $AC=\sqrt{(2+2)^{2} +(5-7)^{2}+(1+3)^{2} }$

By simplifing it we will get $AC=\sqrt{(2+2)^{2} +(5-7)^{2}+(1+3)^{2} }=\sqrt{(16+16+4)} =6$

Now we have to get the value of $R$ .

$R=\frac{1}{2} \times 6=3$

Therefore $R+P_{y} =3+4=7$

The final answer is $7$

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