Construction of angle of 90°
Steps of construction:
Step 2: With its initial point O as center and any radius, draw an arc, cutting OA at C.
Step 3: With center c and same radius (as in step 2) draw an arc cutting arc at D.
Step 4: With D as center and the same radius, draw an arc cutting the arc cutting at E.
Step 5: With D and E as centers and any convenient radius (more than DE). Draw to two arcs intersecting at P.
Step 6: Join OP. Then ∠AOP = 90°
By construction, OC = CD = OD
Therefore, ΔOCD is an equilateral triangle. So, ∠COD = 60°
Again OD = DE = OE
Therefore, ΔODE is also an equilateral triangle. So, ∠DOE = 60°
Since, OP bisects ∠DOE, so ∠POD = 30°.
∠AOP = ∠COD + ∠DOP
= 60° + 30°
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