Question

the diameter CD of a circle with Centre O is perpendicular to chord AB if ABis equal to 12 cm and CE=3cm, calculate the radius of the circle

Answer 1

Answer:

7.5 cm

Step-by-step explanation:

Join OA

Now, we have given that

OE = r-3

AE = 1/2 of AB = 6 cm

Now, apply Pythagoras theorem

h² = b² + p²

(OA)² = (AE)² + (OE)²

(r)² = (6)² + ( r-3)²

r² = 36 + r²- 6r + 9

6r = 45

r = 45/6

r = 7.5 cm

Answer 2

Diameter (Double Radius) is 15 cm

Step-by-step explanation:

Given :  

CE = 3cm ; AE = 6 cm $(= \frac {1}{2}AB)$

Let Radius of circle be r so,  

OA = r and OE = (r −3)  

Apply pythagoras theorem in Δ OEA,

$OA^2 = (OE)^2+(AE)^2$

(As In any Right Angled Triangle-

$(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2)$

$r^2= (r-3)^2+6^2$

$r^2=r^2 + 9-6r + 36$

$-6r = -45$

$r= \frac {45}{6}$

r = 7.5 cm

So, Radius of Circle is 7.5 cm

And Hence, Diameter (Double of radius) = 15 cm.