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Point, Lines, Plane and Solids

Properties of...

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Properties of nine point circle and pedal triangle

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Q. Orthocentre of a triangle is

(2, 1)

and the circumcentre is

(\frac{7}{2}, \frac{5}{2})

then its nine points circle centre is..

Q. The circumradius of a triangle is 3.5 cm. Then the radius of the nine-point circle is

Q. The diameter of the nine point circle of the triangle with vertices

(3, 4), (5 cos θ, 5 sin θ)

(5 cos θ, - 5 sin θ)

θ \in R

R_{1}

is the circumradius of the pedal triangle of a given triangle

A B C,

R_{2}

is the circumradius of the pedal triangle of the pedal triangle formed, and so on

R_{3}

R_{4}, . . . . .

then the value of

\infty \sum i = 1 R_{i}

R

(circumradius) of

Δ A B C

= 5

Q. The pedal equation of the circle

x^{2} + y^{2} = 4

with regard to the point

(2, 0)

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