Question : Chords $\overset{―}{A B}$ and $\overset{―}{C D}$ of a circle intersect inside the circle at point F. If $m (\overset{―}{A F}) = 2.4$ cm, $m (\overset{―}{B F}) = 1.8$ cm and $m (\overset{―}{C D}) = 5.7$ cm, what is the length (in cm) of the longer of the two line segments, $\overset{―}{C F}$ and $\overset{―}{D F}$ ?
Option 1: 4.5
Option 2: 4.8
Option 3: 5.4
Option 4: 3.6

Question

Question : $\overset{―}{CT}$ is a tangent to a circle at the point $T$ on the circle. Chord $\overset{―}{AB}$ of the circle is extended to meet the tangent $\overset{―}{CT}$ at the point $C$ . If $m (\overset{―}{AB}) = 3 cm$ and $m (\overset{―}{BC}) = 2.4 cm$ , find the length (in $cm$ ) of the tangent $\overset{―}{CT}$ .
Option 1: 4.2
Option 2: 3.6
Option 3: 3.2
Option 4: 4.0

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Answer 1

Correct Answer: 4.8

Solution :
$m (\overset{―}{A F}) = 2.4$ cm
$m (\overset{―}{B F}) = 1.8$ cm
$m (\overset{―}{C D}) = 5.7$ cm
Let CF = $x$ cm
DF = ( $5.7 - x$ ) cm
Since AB and CD are two chords of a circle that intersect at point F,
AF × BF = CF × DF
⇒ 2.4 × 1.8 = $x$ × ( $5.7 - x$ )
$∴ x$ = 4.8, 0.9
CF = 4.8, DF = 0.9 or,
CF = 0.9, DF = 4.8
$∴$ Longest value = 4.8
Hence, the correct answer is 4.8.

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Question : Chords AB― and CD― of a circle intersect inside the circle at point F. If m(AF―)=2.4 cm, m(BF―)=1.8 cm and m(CD―)=5.7 cm, what is the length (in cm) of the longer of the two line segments, CF― and DF―?Option 1: 4.5Option 2: 4.8Option 3: 5.4Option 4: 3.6

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