One and only one circle can pass through three non-collinear points.

Correct Option: A

On the basis of given question ,
We can say that One and only one circle can pass through three non-collinear points.

As per the given in question , we draw a figure of a circle with centre O,

OC ⊥ AB
∴ AC = CB
OA = 13 cm. , OC = 12 cm.
In ∆ OAC, AC = √OA² - OC²
AC = √13² - 12²

Correct Option: A

As per the given in question , we draw a figure of a circle with centre O,

OC ⊥ AB
∴ AC = CB
OA = 13 cm. , OC = 12 cm.
In ∆ OAC, AC = √OA² - OC²
AC = √13² - 12²
AC = √(13 + 12)(13 - 12)
AC = √25 = 5 cm.
∴ AB = 2 AC = 10 cm.

According to question , we draw a figure of a circle with centre O ,

In ∆ PQR,
∠PQR = 40° ; ∠QRP = 60°
∴ ∠QPR = 180° – 60° – 40° = 80°

Correct Option: D

According to question , we draw a figure of a circle with centre O ,

In ∆ PQR,
∠PQR = 40° ; ∠QRP = 60°
∴ ∠QPR = 180° – 60° – 40° = 80°
∴ Angle subtended at the circumference by arc QR = 80°
∴ Angle subtended at the centre by arc QR = ∠QOR = 2∠QPR = 2 × 80° = 160°

On the basis of question we draw a figure of two circles touch each other externally ,

Correct Option: A

On the basis of question we draw a figure of two circles touch each other externally ,

We know that , Distance between two circles = OO' = r₁ + r₂ = 7 cm.
r₁ = 4 cm.
∴ r₂ = (7 – 4) cm. = 3 cm.

On the basis of question we draw a figure of a circle with centre O and radius is 5 cm ,

Here , OA = radius = 5 cm.
OC ⊥ AB

Correct Option: B

On the basis of question we draw a figure of a circle with centre O and radius is 5 cm ,

Here , OA = radius = 5 cm.
OC ⊥ AB