Question

Given a circle of radius 5 cm and center o. om is drawn perpendicular to the chord xy. If I'm =3 cm, then length of chord xy is -​

Answer 1

brainliest. f thanks me plsss

The diagram is bad but understand...

5 cm is radius so that becomes hypotenuse of OAM.

So, OM - 4cm OA-5 cm

OA²=OM² + AM² (Pythagoras Theorem)

5² = 4² + AM²

25 = 16 + AM²

25 - 16 = AM²

9 = AM²

√9 = AM

3 = AM.

Now AM = BM since the two s are congruent. OM is common side, OA = OB = Radius of circle.

So, AM=BM=3cm

so AB = AM + BM = 3+3 = 6cm.

Answer 2

The length of the chord XY according to the question conditions is 8 cm.

Given :

Radius of the Circle = 5 cm

Length of Perpendicular on chord XY = 3 cm

To Find :

Length of the chord XY

Solution :

It is given that the center of the circle is at O. The chord XY is drawn and a perpendicular OM of length 3cm is drawn on the chord. So, OMX forms a right-angled triangle with :

OM ( Perpendicular ) = 3 cm

OX ( Radius of the circle ) = 5 cm

Applying Pythagoras formula,

            $(MX)^{2} + (OM)^{2} = (OX)^{2}$

            $(MX)^{2} = (OX)^{2} - (OM)^{2}$

                         $= 5^{2} - 3^{2}$

                         $= 25 - 9$

                         $= 16$

              $\sqrt{MX^{2} } = \sqrt{16}$

                 $MX = 4$

Perpendicular from the center of the circle divides the chord into equal halves. Thus, $XM = MY$

Length of the chord XY $= XM + YM$

                                        $= 2 * MX$

                                        $= 2 * 4$

                                        $= 8$

Hence, the length of the chord XY is 8 cm.

To learn more about Chord, visit

https://brainly.in/question/18734476

#SPJ2