given below is a circle with centre O and DE is an arc of a circle with centre B. If BC=1 cm and BE=Root5 cm, what is the length of OB
Answers
Given :- A circle with centre O and DE is an arc of a circle with centre B. If BC = 1 cm and BE = √5 cm, what is the length of OB ?
Solution :-
In right angled ∆BCE we have,
→ BE = √5 cm (given)
→ BC = 1 cm (given)
so,
→ CE = √[(√5)² - 1¹] { using pythagoras theorem. }
→ CE = √(5 - 1) = √4 = 2 cm .
now, we have,
→ OD = OB { radius of circle. }
→ OD = (OC + 1)
and,
→ DC = CE { Line from centre to the chord bisect the chort at 90°. }
then , in right angled ∆ODC, we have,
→ OD² = OC² + DC²
→ (OC + 1)² = OC² + 2²
→ OC² + 1 + 2*OC = OC² + 4
→ 2*OC = 3
→ OC = (3/2) cm .
therefore,
→ OB = OC + 1 = (3/2) + 1 = (5/2) = 2.5 cm (Ans.)
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