Question

Find the length of a chord, which is at a distance of 5 cm from the

centre of a circle of radius 13 cm. 9th standard ​

Answer 1

Answer:

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Let OA and OB be the radius of the circle

And AB be the chord

Also OD be the distance from the centre of the circle to the radius.

Given

radius=13.

distance=5

Now

In right triangle ODB,

OD²+DB²=OB²

In right triangle ODB, OD²+DB²=OB² 5²+DB² =13²

In right triangle ODB, OD²+DB²=OB² 5²+DB² =13² 25+DB²=169

In right triangle ODB, OD²+DB²=OB² 5²+DB² =13² 25+DB²=169 DB²=169-25

In right triangle ODB, OD²+DB²=OB² 5²+DB² =13² 25+DB²=169 DB²=169-25 DB²=144

In right triangle ODB, OD²+DB²=OB² 5²+DB² =13² 25+DB²=169 DB²=169-25 DB²=144 DB=√144

DB=12

**DB=DA(taking OD as an altitude which divides it equally)

therefore the length of the chord = DB+DA

=12+12=24

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