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Exercise – 17

Q. 1. Find the point which is equidistant from three given non-collinear points. Give the point a specific name. Justify your answer.

Q. 2. Construct a triangle ABC with AB = 7cm, BC = 8cm and Locate by construction, the point P such that P is equidistant from B and C, and P is equidistant from AB and BC. Measure the length PB.

Q. 3. Construct a triangle ABC is in which BC = 6cm, AB = 9cm and

1. Construct the locus of all points inside triangle ABC, which are equidistant from B and C.
2. Construct the locus of the vertices of the triangle with BC as base, which are equal in area to triangle ABC.
3. Marks the point Q in your construction which would make triangle QBC equal in area to triangle ABC and isosceles.
4. Measure length CQ.

Q. 4. Construct a triangle ABC with AB = 6cm, and BP = 5cm. Complete the rectangle ABCD such that

1. P is equidistant from AB and BC, and
2. P is equidistant from A and D

Q. 5. Construct a with CB = 5cm, and BP = 4cm. Complete the rectangle ABCD such that

1. P is equidistant from AB and BC, and
2. P is equidistant from C and D

Q. 6. Using only a ruler and compasses construct , where AB = BC = 5cm.

1. Mark two points D and E which satisfy the condition that they are equidistant from both BA and BC.
2. In the above figure, join AE and EC. Describe the figures
   1. ABCD
   2. BD
   3. ABE

Q. 7. Using a ruler and compass only

1. Construct a triangle ABC with BC = 6cm, and AB = 3.5cm
2. In the above figure, draw a circle with BC as diameter. Find a point ‘P’ on the circumference of the circle which is equidistant from AB and BC Measure .

Q. 8. Use a ruler and a pair of compasses to construct in which BC = 4.2cm, and AB = 5cm. Construct a circle of radius 2cm to touch both the arms of .

Q. 9. Construct an isosceles such that AB = 6cm, BC = AC = 4cm. Bisect internally and mark a point P on this bisector such that CP = 5cm. Find the points Q and R which are 5cm away from P and also 5cm from the line AB.

Q. 10. Use graph paper for this question: Take 2cm = 1 unit on both axes:

1. Plot the points A(1, 1), B (5, 3) and C (3, 7)
2. Construct the locus of points equidistant from A and B.
3. Construct the locus of points equidistant from AB and AC
4. Locate the point P such that PA = PB and P is equidistant from AB and AC
5. Measure and record the length of PA in cm.

Q. 11. Ruler and compass 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.

1. Construct , in which BC= 8cm, AB = 5cm and
2. Construct the locus of points inside the triangle which are equidistant from BA and BC
3. Construct the locus of points inside the triangle which are equidistant from B and C
4. Mark as P, the point which is equidistant from AB, BC and also equidistant from B and C
5. Measure and record the length of PB.