Question

Theorem 10.5:- there is one and only one circle passing through three given non- collinear points. Prove that
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Answer 1

Step by step explained...

Answer 2

Hence proved that one and only one circle passing through three non- collinear points.

Step-by-step explanation:

Given,

Three non-collinear points P, Q, and R.

To prove,

There is only one circle that could be constructed through these points P, Q, and R.

Proof:

Because O exists on the perpendicular bisector of PQ,

OP = OQ

Because O exists on the perpendicular bise-ctor of QR,

OQ = OR

∵ OP = OQ = OR and O is at equal distant from P, Q, and R.

If a circle is drawn using OP as the radius, it will surely pa-ss through Q and R.

Because perpendicular bisectors of PQ and QR intersect one another at O only.

Since O is the point having equal distance from P, Q, and R. Thus, only once circle can be drawn passing through all three non-collinear points.

Learn more: Non-Collinear points

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