Describe completely the locus of centre of a circle of varying radius and touching two arms of ∠ABC.

Let there be two circles with centre O and O' and BD be the angle bisector of ∠ABC. AB and BC are two tangents to the circle. We know that radius and tangent make 90°. From graph, ∠OEB = ∠OFB (Both are equal to 90) ∠OBE = ∠OBF (Since, BX is the angle bisector of ∠ABC.) Hence, by AA axiom △OEB ~ △OFB. Since triangles are similar hence, the ratio of their corresponding sides are similar. Since, O is the centre hence, we can say that OE = OF = radius. Thus circle with centre O is at equal distance from both arms of angle. Similarly, From graph, ∠O'GB = ∠O'HB (Both are equal to 90) ∠O'BG = ∠O'BH (Since, BX is the angle bisector of ∠ABC.) Hence, by AA axiom △O'GB ~ △O'HB. Since triangles are similar hence, the ratio of their corresponding sides are similar. Since, O' is the centre hence, we can say that O'G = O'H = radius. Thus circle with centre O' is at equal distance from both arms of angle. Hence, the locus is the bisector of the ∠ABC.

Describe completely the locus of point in a plane equidistant from a given line.

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Describe completely the locus of point in a plane, at a constant distance of 5 cm from a fixed point (in the plane).

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Describe completely the locus of centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O.

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Using ruler and compasses, construct
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of points equidistant from A and C.

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Mathematics

Describe completely the locus of centre of a circle of varying radius and touching two arms of ∠ABC.

Locus

Related Questions

Describe completely the locus of point in a plane equidistant from a given line.

Describe completely the locus of point in a plane, at a constant distance of 5 cm from a fixed point (in the plane).

Describe completely the locus of centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O.

Using ruler and compasses, construct
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of points equidistant from A and C.

Mathematics

Describe completely the locus of centre of a circle of varying radius and touching two arms of ∠ABC.

Locus

Related Questions

Describe completely the locus of point in a plane equidistant from a given line.

Describe completely the locus of point in a plane, at a constant distance of 5 cm from a fixed point (in the plane).

Describe completely the locus of centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O.

Using ruler and compasses, construct(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.(ii) the locus of points equidistant from A and C.

Using ruler and compasses, construct
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of points equidistant from A and C.