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Using only ruler and compasses, let us construct a triangle ABC, with $AB=5cm$, $BC=3.5cm$ and $AC=4cm$. Mark a point P, which is equidistant from AB, BC and also from B and C. So we need to measure the length of PB.
Using only ruler and compasses, let us construct a triangle ABC, with $AB=5cm$, $BC=3.5cm$ and $AC=4cm$. Mark a point P, which is equidistant from AB, BC and also from B and C. So we need to measure the length of PB.
Class 10 | Frank | Guides | ICSE | Loci | Maths
Using only ruler and compasses, let us construct a triangle ABC, with $AB=5cm$, $BC=3.5cm$ and $AC=4cm$. Mark a point P, which is equidistant from AB, BC and also from B and C. So we need to measure the length of PB.

Steps of construction:

1. Draw a line segment $BC=3.5cm$.

2. With B as a center and radius $5cm$, let’s draw an arc using compass.

3. With C as a center and radius $4cm$, draw another arc using compass, cutting the previous arc at A.

4. So now Join AB and AC.

Then, $\vartriangle ABC$ is the required triangle.

5. With B as center and radius measuring more than half of BC, draw arcs using compass on both sides of BC.

6. With C as center and the same radius as before, draw arcs using compass on both sides of BC, cutting the previous arcs with the help of compass at P and Q, as shown. Now Join PQ.

Then, PQ is the required perpendicular bisector of BC.

Therefore , We get P is the required point which is at equal distance  from AB, BC, B and C.

So the Length PB is $2.5cm$.

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