- A15 cm
- B10 cm
- C25 cm
- D20 cm
Step-by-Step Solution
AC and AD are radii of the circle centred A, so each is 5 cm; BC and BD are radii of the circle centred B, so each is 5 cm. Perimeter cm (15 cm is only triangle ABC).
Answer: D) 20 cm
Using Euclid's construction, circles with centres A and B and radius AB = 5 cm are drawn; they meet at C and D. What is the perimeter of the quadrilateral ACBD?
Class 9Introduction to Euclid's GeometryGeometry — Foundations
Key idea: The five postulates of Euclid
**Postulate 1**: A straight line may be drawn from any one point to any other point.
**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).
**Postulate 3**: A circle can be drawn with any centre and any radius.
**Postulate 4**: All right angles are equal to one another.
**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
These 5 statements are the seeds. Everything else in classical geometry grows from them.
**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).
**Postulate 3**: A circle can be drawn with any centre and any radius.
**Postulate 4**: All right angles are equal to one another.
**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
These 5 statements are the seeds. Everything else in classical geometry grows from them.
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