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Constructions (Circles) — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsConstructions (Circles)4 Marks
Question
Using a ruler and a compass construct a triangle ABC in which AB = 7 cm, ∠CAB = 60o and
AC = 5 cm. Construct the locus of
1) points equidistant from AB and AC
2) points equidistant from BA and BC
Hence construct a circle touching the three sides of the triangle internally.
✓

Answer

Steps of construction:
  1. Draw a line AB = 7 cm
  2. Taking P ascentre and same radius, draw an arc of a circle which intersects AB at M.
  3. Taking M ascentre and with the same radius as before drawn an arc intersecting previously drawn arc, at point N.
  4. Draw the ray AX passing through N, then
  5. Taking A ascentre and radius equal to 5 cm, draw an arc cutting AX at C.
  6. Join BC
  7. The required triangle ABC is obtained.
  8. Draw angle bisector of∠CAB and ∠ABC
  9. Mark their intersection as O
  10. With O as center, draw a circle with radius OD
    Image

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