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Question
Using ruler and compasses only,
- Construct a triangle ABC with the following data :
Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°. - In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
- Draw a perpendicular from O to AB which meets AB in D.
- Prove that : AD = BD.
Solution
Steps of construction:
- Draw a line segment AB = 6 cm
- At A, draw a ray making an angle of 60° with BC.
- With B as centre and radius = 6.2 cm draw an arc which intersects AX ray at C.
- Join BC.
ΔABC is the required triangle. - Draw the perpendicular bisectors of AB and AC intersecting each other at O.
- With centre O, and radius as OA or OB or OC, draw a circle which will pass through A, B and C.
- 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.)
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