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Three distinct points A, B and C are given in the 2-dimensiona

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Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(- 1, 0)$ is equal to $\frac{1}{3}$ . Then the circumcentre of the triangle ABC is at the point:

(\frac{5}{2}, 0)

(\frac{5}{3}, 0)

(0, 0)

(\frac{5}{8}, 0)

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Isabella Discussed

Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point

(1, 0)

to the distance from the point

(- 1, 0)

is equal to

\frac{1}{3}

. Then the circumcentre of the triangle ABC is at the point:

13 mins ago

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13 mins ago

Text solutionVerified

Let (h,k) be the locus of points A, B & C

using given condition

\frac{( h - 1 ) ^{2} + K ^{2}}{( h + 1 ) ^{2} + K ^{2}} = \frac{1}{3}

9 (h - 1)^{2} + 9 K^{2} = (h + 1)^{2} + K^{2}

or,

8 h^{2} + 8 K^{2} - 20 h + 8 = 0

h^{2} + K^{2} - \frac{5 h}{4} + 1 = 0

this is a circle and it will be same circle which circumscribe

Δ A BC

as it contains all three pts on it.

∴

center of circumcircle

\equiv (\frac{5}{8}, 0)

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Question Text	Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(- 1, 0)$ is equal to $\frac{1}{3}$ . Then the circumcentre of the triangle ABC is at the point:
Answer Type	Text solution:1
Upvotes	150

Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1,0) to the distance from the point (−1,0) is equal to 31​. Then the circumcentre of the triangle ABC is at the point:

Text solutionVerified

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Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(- 1, 0)$ is equal to $\frac{1}{3}$ . Then the circumcentre of the triangle ABC is at the point: