Advertisements
Advertisements
प्रश्न
The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.
Prove that:
F is equidistant from A and B.
Advertisements
उत्तर
Construction: Join FB and FC
Proof: In ΔAFE and ΔFBE,
AE = EB ...(E is the mid-point of AB)
∠FEA = ∠FEB ...(Each = 90°)
FE = FE ...(Common)
∴ By side Angle side criterion of congruence,
ΔAFE ≅ ΔFBE ...(SAS Postulate)
The corresponding parts of the congruent triangles are congruent.
∴ AF = FB ...(C.P.C.T.)
Hence, F is equidistant from A and B.
APPEARS IN
संबंधित प्रश्न
Draw a line AB = 6 cm. Draw the locus of all the points which are equidistant from A and B.
Describe the locus for questions 1 to 13 given below:
1. The locus of a point at a distant 3 cm from a fixed point.
Describe the locus of a stone dropped from the top of a tower.
The speed of sound is 332 metres per second. A gun is fired. Describe the locus of all the people on the earth’s surface, who hear the sound exactly one second later.
Describe the locus of points at distances greater than 4 cm from a given point.
Draw a triangle ABC in which AB = 6 cm, BC = 4.5 cm and AC = 5 cm. Draw and label:
- the locus of the centres of all circles which touch AB and AC,
- the locus of the centres of all the circles of radius 2 cm which touch AB.
Hence, construct the circle of radius 2 cm which touches AB and AC .
Prove that the common chord of two intersecting circles is bisected at right angles by the line of centres.
Find the locus of the centre of a circle of radius r touching externally a circle of radius R.
ΔPBC, ΔQBC and ΔRBC are three isosceles triangles on the same base BC. Show that P, Q and R are collinear.
The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect in P. Show that P is equidistant from the opposite sides AB and CD.
