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In the figure, O is the centre of circle...

In the figure, O is the centre of circle `/_ QPR = 70^(@)` and m (arc PYR ) `= 160^(@)`, then find the value of each of the following `:`
(a) m ( arc QXR )
(b) `/_QOR`
(c ) `/_ PQR `

Text Solution

Verified by Experts

The correct Answer is:
(a) m ( arc QXR ) 140 (b) `/_ QOR = 140^(@)` (c ) `/_ PQR = 80^(@)`
`/_QPR = (1)/(2) ` m (arc QXR ) …(Inscribed angle theorem )
`:. 70 - (1)?92) ` m (arc QXR )
`:. ` m (arc QXR ) `= 70 xx 2 `
`:. ` m (arc QXR `= 140^(@) `
(b) `/_QOR =` m ( arc QXR ) ….(Definition of measure of minor arc )
`:. /_ QOR = 140^(@)`
(c ) ` /_PQR = (1)/(2) ` m ( arc PYR ) ....(Inscribed angle theorem )
`:. /_ PQR = (1)/(2) xx 160^(@)`
` :. /_ PQR = 80^(@)`
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Knowledge Check

  • In the given figure, O is the centre of the circle. angleAOB = 70^(@) , find angleOCD :

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