Question : $\overline{\mathrm{CT}}$ is a tangent to a circle at the point $\mathrm{T}$ on the circle. Chord $\overline{\mathrm{AB}}$ of the circle is extended to meet the tangent $\overline{\mathrm{CT}}$ at the point $\mathrm{C}$. If $\mathrm{m}(\overline{\mathrm{AB}})=3 \mathrm{~cm}$ and $\mathrm{m}(\overline{\mathrm{BC}})=2.4 \mathrm{~cm}$, find the length (in $\mathrm{cm}$ ) of the tangent $\overline{\mathrm{CT}}$.

Option 1: 4.2

Option 2: 3.6

Option 3: 3.2

Option 4: 4.0

Question : Chords AB and CD of a circle intersect at E. If AE = 9 cm, BE = 12 cm, and CE = 3DE, then the length of DE(in cm) is:

Option 1: $\frac{9}{4}$

Option 2: $4$

Option 3: $6$

Option 4: $7$

Question : In a triangle DEF, DP is the bisector of $\angle D$, meeting EF at P. If DE = 14 cm, DF = 21 cm and EF = 9 cm, find EP.

Option 1: 3.6 cm

Option 2: 5.4 cm

Option 3: 6.3 cm

Option 4: 2.7 cm

Question : In a circle, two chords $AB$ and $CD$ intersect each other internally at point $P$. If $AB=16\; cm, PB =6\;cm $, and $PD =12\; cm$, then the value of $PC$ (in $cm $) is equal to:

Option 1: 3

Option 2: 8

Option 3: 6

Option 4: 5

Question : BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm, and CF = 4 cm. Then, the length of BE is:

Option 1: 4.8 cm

Option 2: 7.5 cm

Option 3: 3.33 cm

Option 4: 5.5 cm