Question

Using ruler and compasses only,

1. Construct a triangle ABC with the following data :
   Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°.
2. In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
3. Draw a perpendicular from O to AB which meets AB in D.
4. Prove that : AD = BD.

Answer 1

 
Steps of construction:

1. Draw a line segment AB = 6 cm
2. At A, draw a ray making an angle of 60° with BC.
3. With B as centre and radius = 6.2 cm draw an arc which intersects AX ray at C.
4. Join BC.
   ΔABC is the required triangle.
5. Draw the perpendicular bisectors of AB and AC intersecting each other at O.
6. With centre O, and radius as OA or OB or OC, draw a circle which will pass through A, B and C. 
7. From O, draw OD ⊥ AB.

Proof: In right ΔOAD and ΔOBD

OA = OB  ...(Radii of same circle)

Side OD = OD  ...(Common)

∴ ΔOAD ≅ ΔOBD  ...(R.H.S.)

`=>` AD = BD  ...(C.P.C.T.)