Chords AB and CD of a circle interest at E and are perpendicular to each other. Segments AE, EB and ED are of lengths 2 cm, 6 cm and 3 cm respectively. Then the length of the diameter the circle in cm is :

Options

A. `sqrt(65)`
B. `(1)/(2) sqrt(65)`
C. 65
D. `(65)/(2)`

Answer

A

Explanation

दिया है

`AE=2cm, EB= 6cm, ED=3 cm`
`:. AExx EB= CExx ED`
`rArr CE=4 cm`
`angleCEB=angleCDB=90^(@)=` (अर्धवृत्त का कोण समकोण होता है)
`angleCDB ~=angleCEB`
`rArr DB=CE=4 cm`
समकोण `DeltaBCD` में,
`CD^(2)+BD^(2)=BC^(2)`
`rArr 7^(2)+4^(2)=BC^(2)`
`rArr BC= sqrt(49+16)`
`rArr BC= sqrt(65)`
अतः वृत्त का व्यास `sqrt (165) cm` होगा।