Advertisements
Advertisements
प्रश्न
In the given figure ABC is a triangle. CP bisects angle ACB and MN is perpendicular bisector of BC. MN cuts CP at Q. Prove Q is equidistant from B and C, and also that Q is equidistant from BC and AC.
Advertisements
उत्तर
Join BQ and draw perpendicular bisector of AC cutting AC at L.
In Δ QBN and ΔQCN
QN = QN
BN =NC
∠ QNB = ∠ QNC = 90 degree.
Therefore, ∠ QBN and ∠.QCN are congruent .
Hence Q is equidistant from B and C.
In Δ QNC and Δ QLC
QC= QC
∠ QLC = ∠ QNC = 90 degree.
∠ QCL =∠ QCN (PC being angle bisector)
Therefore, .Δ QNC and Δ QLC are congruent.
Therefore, QL = QN.
Hence Q is equidistant from BC and AC.
APPEARS IN
संबंधित प्रश्न
On a graph paper, draw the line x = 6. Now, on the same graph paper, draw the locus of the point which moves in such a way that its distantce from the given line is always equal to 3 units
Describe the locus of a point in space, which is always at a distance of 4 cm from a fixed point.
Construct a triangle ABC, with AB = 5.6 cm, AC = BC = 9.2 cm. Find the points equidistant from AB and AC; and also 2 cm from BC. Measure the distance between the two points obtained.
Use graph paper for this question. Take 2 cm = 1 unit on both the axes.
- Plot the points A(1, 1), B(5, 3) and C(2, 7).
- Construct the locus of points equidistant from A and B.
- Construct the locus of points equidistant from AB and AC.
- Locate the point P such that PA = PB and P is equidistant from AB and AC.
- Measure and record the length PA in cm.
Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these Iines and also 2 cm away from their point of intersection. How many such points exist?
A and B are fixed points while Pis a moving point, moving in a way that it is always equidistant from A and B. What is the locus of the path traced out by the pcint P?
In given figure, ABCD is a kite. AB = AD and BC =CD. Prove that the diagona AC is the perpendirular bisector of the diagonal BD.
In given figure 1 ABCD is an arrowhead. AB = AD and BC = CD. Prove th at AC produced bisects BD at right angles at the point M
State and draw the locus of a point equidistant from two given parallel lines.
Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords, AB and AC, of the circle of length 6 cm and 5 cm respectively.
- Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.
- Construct the locus of points, inside the circle, that are equidistant from AB and AC.
