ICSE Class 10th Mathematics Chapter 16 - Loci Important Questions with Answers

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Given: PQ is perpendicular bisector of side AB of the triangle ABC.

Prove: Q is equidistant from A and B.

Question 2.

Given: CP is bisector of angle C of ?ABC.

Prove: P is equidistant from AC and BC.

Question 3.

Given: AX bisects angle BAC and PQ is perpendicular bisector of AC which meets AX at point Y.

Prove:

X is equidistant from AB and AC.
Y is equidistant from A and C.

Question 4.

Construct a triangle ABC, in which AB = 4.2 cm, BC = 6.3 cm and AC = 5 cm. Draw perpendicular bisector of BC which meets AC at point D. Prove that D is equidistant from B and C.

Question 5.

In each of the given figures; PA = PB and QA = QB.

i.
ii.

Prove, in each case, that PQ (produce, if required) is perpendicular bisector of AB. Hence, state the locus of the points equidistant from two given fixed points.

Question 6.

Construct a right angled triangle PQR, in which ?Q = 90°, hypotenuse PR = 8 cm and QR = 4.5 cm. Draw bisector of angle PQR and let it meets PR at point T. Prove that T is equidistant from PQ and QR.

Question 7.

Construct a triangle ABC in which angle ABC = 75°, AB = 5 cm and BC = 6.4 cm. Draw perpendicular bisector of side BC and also the bisector of angle ACB. If these bisectors intersect each other at point P; prove that P is equidistant from B and C; and also from AC and BC.

Question 8.

In parallelogram ABCD, side AB is greater than side BC and P is a point in AC such that PB bisects angle B. Prove that P is equidistant from AB and BC.

Question 9.

In triangle LMN, bisectors of interior angles at L and N intersect each other at point A. Prove that:

Point A is equidistant from all the three sides of the triangle.
AM bisects angle LMN.

Question 10.

Use ruler and compasses only for this question.

Construct ?ABC, where AB = 3.5 cm, BC = 6 cm and ?ABC = 60°.
Construct the locus of points inside the triangle which are equidistant from BA and BC.
Construct the locus of points inside the triangle which are equidistant from B and C.
Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.