Circles Maths - Circles

In the given figure, $O$ is the centre of a circle, $P Q$ is a chord and $P T$ is the tangent at $P, \angle P O Q=70^{\circ}$, then $\angle T P Q$ is equal to

• A
  $55^{\circ}$
• B
  $70^{\circ}$
• C
  $45^{\circ}$
• ✓
  $35^{\circ}$

Answer: D.

• A
  $5 \sqrt{2}$
• ✓
  $10 \sqrt{2}$
• C
  $\frac{5}{\sqrt{2}}$
• D
  $10 \sqrt{3}$

Answer: B.

In the given figure, there are two concentric circles of radii $6 \ cm$ and $4 \ cm$ with centre $O$. If $A P$ is a tangent to the larger circle and $B P$ to the smaller circle and length of $A P$ is $8 \ cm$, then the length of $B P$ is

• A
  $21 cm$
• B
  26
• ✓
  $2 \sqrt{21} cm$
• D
  None of these

Answer: C.

• A
  $\sqrt{7} cm$
• ✓
  $2 \sqrt{7} cm$
• C
  $10 cm$
• D
  $5 cm$

Answer: B.

In the given figure, $P A$ and $P B$ are tangents to the circle from an external point $P . C D$ is another tangent touching the circle at $Q$. If $P A=12 cm , Q C=Q D=3 cm$ then the value of $P C$ is

• A
  $6 cm$
• ✓
  $9 cm$
• C
  $12 cm$
• D
  $3 cm$

Answer: B.