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In a cyclic quadrilateral PQRS, PQ= 2 un...

In a cyclic quadrilateral PQRS, PQ= 2 units, QR= 5 units, RS=3 units and `/_P Q R=60^0,` then what is the measure of SP?

Text Solution

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From `Delta PQR, PR^(2) = 2^(2) + 5^(2) - 2 xx 5 xx 2 xx cos 60^(@) = 19`

In `Delta PRS, PR^(2) = 3^(2) + x^(2) - 2 xx 3x xx cos 120^(2)` (where SP = x)
`rArr x^(2) + 3x + 9 = 19`
`rArr (x + 5) (x - 2) = 0`
Now, `x + 5 = 0` not possible
`:. x = 2`
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