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Joint Entrance Examination
Mathematics
Circle
Question 4
Question 4 of 219
Medium
NUMERICAL
Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line
x
+
y
=
1
x + y = 1
x
+
y
=
1
is
14
\sqrt{14}
14
, then ... Answer: 8
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Official solution
r
2
=
(
14
2
)
2
+
(
r
−
1
2
)
2
r
2
=
7
2
+
r
2
−
2
r
+
1
2
2
r
=
4
r
=
2
2
r
2
=
8
\begin{gathered} {r}^{2}={(\frac{\sqrt{14}}{2})}^{2}+{(r-\frac{1}{\sqrt{2}})}^{2} \\ {r}^{2}=\frac{7}{2}+{r}^{2}-\sqrt{2}r+\frac{1}{2} \\ \sqrt{2}r=4 \\ r=2\sqrt{2} \\ {r}^{2}=8 \end{gathered}
r
2
=
(
2
14
)
2
+
(
r
−
2
1
)
2
r
2
=
2
7
+
r
2
−
2
r
+
2
1
2
r
=
4
r
=
2
2
r
2
=
8
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