Find y in the figure below;
Solution
From circle geometry,
(QR)(QS) = (PQ)2
y(y + 21) = 102
y2 + 21y = 100
y2 + 21y – 100 = 0
We factorize by splitting the middle term: 21y = (25y – 4y).
y2 + 25y – 4y – 100 = 0
(y2 + 25y) – (4y – 100) = 0
y(y + 25) – 4(y + 25) = 0
(y - 4)( y + 25) = 0
y - 4 = 0 OR
y + 25 = 0
y = 4 OR y = -25
Since we
don’t have negative length, we take y = 4cm
TRY THIS……..
Find y in the figure below;
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