Question

two parallel cords of a circle are 6 cm and 8 cm in length. if they are 7 cm

apart, find the radius of the circle​

Answer 1

$\huge{\orange{\underline{\underline{\bf{☆\;SoluTion:}}}}}$

Let's

AB and CD are two parallel chords of a circle having length 6 cm and 8 cm and radius is O.

Let the radius of the circle be r.

Now draw OP perpendicular to AB and OQ perpendicular to CD.

Since, OP is perpendicular to AB and OQ is perpendicular to CD and AB || CD

From figure, OP = 4 cm.

P, Q are the mid points of AB and CD respectively.   

[perpendicular  from center bisects the chord]

$\sf{So, AP = PB = \frac{AB}{2}}$

$→\;{\sf{\frac{6}{2} = 3cm}}$

$\bf{CQ = QD = \frac{CD}{2}}$

$→\;{\bf{\frac{8}{2} = 4cm}}$

Now, In ∆le OAP

Angle OPA = 90°

By Pythogras Theorem

$\boxed{\bf{(Hypothenuse)² = (Side)² + (Side)²}}$

$→\;{\sf{r² = 4²+3²}}$

$→\;{\sf{r² = 16+9}}$

$→\;{\sf{r = \sqrt{25}}}$

$→\;{\sf{r = \sqrt{5²}}}$

$☞\;{\red{\sf{Radius = 5cm}}}$

_______________________

Refer The 2nd Attachment For Method 2

Hope It Helps You ✌️

Answer 2

Step-by-step explanation:

Now in ∆OAP

OA² = OP² + AP²

r² = 16 + 9

r = √16 + 9

r = √25

r = 5cm