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

Given , ∠ACB = 65°
∠AOB = 2 × ∠ACB = 2 × 65° = 130°

Correct Option: A

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

Given , ∠ACB = 65°
∠AOB = 2 × ∠ACB = 2 × 65° = 130°
∠OAP = 90°; ∠AOP = 65°
∴ ∠APO = 180° – 90° – 65° = 25°

According to question , we draw a figure of a circle with two chords AB and CD ,

Given , AB = 6 cm; CD = 3 cm
PD = 5 cm; PB = ?
We know that , PA × PB = PC × PD
⇒ (PB – 6) PB = 2 × 5
⇒ PB² – 6PB – 10 = 0

Correct Option: B

According to question , we draw a figure of a circle with two chords AB and CD ,

Given , AB = 6 cm; CD = 3 cm
PD = 5 cm; PB = ?
We know that , PA × PB = PC × PD
⇒ (PB – 6) PB = 2 × 5
⇒ PB² – 6PB – 10 = 0

On the basis of question we draw a figure of two circles with centres O and O' ,

Here , AB = 16 cm and OO' = 12 cm
AC = BC = 8 cm
OC = CƠ = 6 cm
∴ OA = √OC² + CA²
OA = √6² + 8²

Correct Option: A

On the basis of question we draw a figure of two circles with centres O and O' ,

Here , AB = 16 cm and OO' = 12 cm
AC = BC = 8 cm
OC = CƠ = 6 cm
∴ OA = √OC² + CA²
OA = √6² + 8²
OA = √36 + 64
OA = √100 = 10 cm

As per the given in question , we draw a figure circle

Given , AB = 24 cm
⇒ AE = EB = 12 cm
OE = √OA² - AE²
OE = √15² - 12²
OE = √225 - 144 = √81
OE = 9 cm

Correct Option: B

As per the given in question , we draw a figure circle

Given , AB = 24 cm
⇒ AE = EB = 12 cm
OE = √OA² - AE²
OE = √15² - 12²
OE = √225 - 144 = √81
OE = 9 cm
∴ OF = 21 – 9 = 12 cm
Also, CF = √15² - 12² = 9 cm
∴ CD = 2 × CF = 2 × 9 = 18 cm

As per the given question ,
One and only circle can pass through three non-collinear points.

Correct Option: B

As per the given question ,
We can say that One and only circle can pass through three non-collinear points.