Question

in figure 13.3 1 CD is diameter which meets the chord AB in E , such that AE = BE = 4 cm if C is 3 cm find the radius of the circle.​

Answer 1

★ Answer ★

☆ Given :-

• CD is diameter which meets the chord AB in E , such that AE = BE = 4 cm. C is 3 cm.

☆ Find :-

• Find the radius of the circle.

☆ Solution :-

As we know from given that O is the centre of circle.

➹ Let's do Construction :-

Joining OA

According to the Theorem 10.4

The line drawn through the centre of the circle to bisect a chord is perpendicular to the chord.

Now,

Here, AB is chord , OE⊥AB

Let's consider the,OC be xcm = OAOA { Both radii of the circle}

Then, we know one thing that,

OE = OC − EC = (x−3) cm

Therefore , InΔOEA

Applying Pythagoras Theorem

So,

★ OA² = OE² + AE²

x² = ( x − 3 )² + 4²

$\longmapsto\tt{x=\cancel\dfrac{25}{6}}$

x = 4.16cm { Radius of the circle }