Circles Maths - Circles

In the given figure, $\text{QR}$ is a common tangent to the given circles touching externally at the point $T.$ The tangent at $T$ meets $\text{QR}$ at $P.$ If $\text{PT} = 3.8\ cm,$ then the length of $\text{QR} ($ in $cm)$ is:

• A
  $3.8$
• ✓
  $7.6$
• C
  $5.7$
• D
  $1.9$

Answer: B.

In the figure, a quadrilateral $\text{ABCD}$ is drawn to circumscribe a circle such that its sides $\text{AB, BC, CD}$ and $\text{AD}$ touch the circle at $\text{P, Q, R}$ and $S$ respectively. If $\text{AB} = x \ cm,$
$\text{BC}= 7\ cm, \text{CR} = 3\ cm$ and $\text{AS} = 5\ cm,$ then $x =$

• A
  $10$
• ✓
  $9$
• C
  $8$
• D
  $7$

Answer: B.

In the given figure, if $\text{AD, AE}$ and $\text{BC}$ are tangents to the circle at $\text{D, E}$ and $\text{F}$ respectively, Then:

• A
  $\ce{AD = AB + BC + CA}$
• ✓
  $\ce{2AD = AB + BC + CA}$
• C
  $\ce{3AD = AB + BC + CA}$
• D
  $\ce{4AD = AB + BC + CA}$

Answer: B.

• A
  $\sqrt{7}\text{cm}$
• B
  $7\ cm$
• ✓
  $5\ cm$
• D
  $25 \ cm$

Answer: C.

• A
  $30^\circ$
• B
  $60^\circ$
• ✓
  $90^\circ$
• D
  $180^\circ$

Answer: C.