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.
(i) Construct the locus of points, inside the circle, that is equidistant from A and C. Prove your construction.
(ii) Construct the locus of points, inside the circle, that is equidistant from AB and AC, (1995)
Solution:
Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct a triangle ABC, in which BC = 6 cm, AB = 9 cm. and ∠ABC = 60°.
(ii) Construct the locus of all points, inside ∆ABC, which are equidistant from B and C.
(iii) Construct the locus of the vertices of the triangles with BC as a base, which is equal in area to ∆ABC.
(iv) Mark the point Q, in your construction, which would make ∆QBC equal in area to ∆ABC, and isosceles.
(v) Measure and record the length of CQ. (1998)
Solution:
More Solutions:
- Given below, AB is a diameter of a circle with centre O.
- P is the point of intersection of the chords BC and AQ.
- CP bisects ∠ACB. Prove that DP bisects ∠ADB.
- Given below, chords AB and CD of a circle intersect at E.
- AE and BC intersect each other at point D. If ∠CDE = 90°.
- Calculate the perimeter of the cyclic quadrilateral PQRS.