Circles [NEW] Maths - Circles [NEW]

If $A B=12 cm, B C=16 cm$ and $A B$ is perpendicular to $B C$, then the radius of the circle passing through the points A, B and C is

• A
  6 cm
• B
  8 cm
• ✓
  10 cm
• D
  12 cm

Answer: C.

In Fig. two congruent circles have centres $O$ and $O^{\prime}$. Arc AXB subtends an angle of $75^{\circ}$ at the centre $O$ and arc $A^{\prime} Y B^{\prime}$ subtends an angle of $25^{\circ}$ at the centre $O^{\prime}$. Then the ratio of arcs $A X B$ and $A^{\prime} Y B^{\prime}$ is

• A
  $2: 1$
• B
  $1: 2$
• ✓
  $3: 1$
• D
  $1: 3$

Answer: C.

In Fig. if $\angle O A B=40^{\circ}$, then $\angle A C B$ is equal to

• ✓
  $50^{\circ}$
• B
  $40^{\circ}$
• C
  $60^{\circ}$
• D
  $70^{\circ}$

Answer: A.

In Fig. if $\angle D A B=60^{\circ}$ and $\angle A B D=50^{\circ}$, then $\angle A C B=$

• A
  $60^{\circ}$
• B
  $50^{\circ}$
• ✓
  $70^{\circ}$
• D
  $80^{\circ}$

Answer: C.

In Fig. if $\angle A O B$ is a diameter of the circle and $A C=B C$, then $\angle C A B$ is equal to

• A
  $30^{\circ}$
• B
  $60^{\circ}$
• C
  $90^{\circ}$
• ✓
  $45^{\circ}$

Answer: D.

• A
  Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
• B
  Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
• C
  Statement-1 is True, Statement-2 is False.
• ✓
  Statement-1 is False, Statement-2 is True.

Answer: D.

• A
  Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
• B
  Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
• C
  Statement-1 is True, Statement-2 is False.
• ✓
  Statement-1 is False, Statement-2 is True.

Answer: D.

Statement-1 (A): In Fig. $O$ is the centre of a circle and $\angle A O C=140^{\circ}$, then $\angle A B C=110^{\circ}$.
Statement-2 (R): Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

• A
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
• ✓
  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
• C
  Statement-1 is true, Statement-2 is false.
• D
  Statement-1 is false, Statement-2 is true.

Answer: B.

Statement-1 (A): In Fig.(i), if AOB is a diameter and $\angle A D C=120^{\circ}$, then $\angle C A B=30^{\circ}$.
Statement-2 (R): In Fig.(ii), AOB is a diameter and $\angle A D C=120^{\circ}$, then $\angle B A C=30^{\circ}$.

• ✓
  Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
• B
  Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
• C
  Statement-1 is True, Statement-2 is False.
• D
  Statement-1 is False, Statement-2 is True.

Answer: A.

Statement-1 (A): In Fig. if $\angle A O B=100^{\circ}$ and $\angle B O C=120^{\circ}$, then $\angle A B C=70^{\circ}$.
Statement-2 (R): The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

• ✓
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
• B
  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
• C
  Statement-1 is true, Statement-2 is false.
• D
  Statement-1 is false, Statement-2 is true.

Answer: A.