You visited us 1 times! Enjoying our articles? Unlock Full Access!

Angle Subtended by Diameter on the Circle

If AOB is a...

Question

If $A O B$ is a diameter of a circle with center $O$ and $C$ is a point on the circle, then the statement " $A C^{2} + B C^{2} = A B^{2}$ " is

true

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

false

No worries! We‘ve got your back. Try BYJU‘S free classes today!

can not be determined

No worries! We‘ve got your back. Try BYJU‘S free classes today!

true only for some points on the circle.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A true
Angle subtended by the diameter at the circumference of a circle is one right angle.
$A O B$ is diameter and $C$ is a point on the circle.
$∠ A C B = 90^{O}$
Using Pythagoras Theorem, we have
${A C}^{2} + {B C}^{2} = {A B}^{2}$

Suggest Corrections

Similar questions

Q. Question 6
Write True or False and justify your answer :

If AOB is a diameter of a circle and C is a point on the circle, then

A C^{2} + B C^{2} = A B^{2}

Q. Fill In The Blanks

If AOB is a diameter of a circle and C is a point on the circle, then the AC² + BC²= ____________.

Q. Draw a triangle ABC, with AC = 4 cm, BC = 3 cm and ∠C = 80°. Measure AB. Is (AB)² = (AC)² + (BC)²? If not, which one of the following is true:
(AB)² > (AC)² + (BC)² or (AB)² < (AC)² + (BC)²?

In the given figure, A, B and C are three points on the circle with centre O such that $∠ B O C = 30^{\circ}$ and $∠ A O B = 60^{\circ}$ . If D is a point on the circle that is not on the arc ABC, then find $∠ A D C .$

Q. A circle centered at

O

has radius

1

and contains points

A

. Segment

A B

is tangent to the circle at

A

and

∠ A O B = θ

. If point

C

lies on

O A

, and

B C

bisects the

∠ A B O

, then

O C

equals

Join BYJU'S Learning Program

If AOB is a diameter of a circle with center O and C is a point on the circle, then the statement "AC2+BC2=AB2" is

The correct option is A trueAngle subtended by the diameter at the circumference of a circle is one right angle. AOB is diameter and C is a point on the circle.∠ACB=90OUsing Pythagoras Theorem, we haveAC2+BC2=AB2

If $A O B$ is a diameter of a circle with center $O$ and $C$ is a point on the circle, then the statement " $A C^{2} + B C^{2} = A B^{2}$ " is

The correct option is A true
Angle subtended by the diameter at the circumference of a circle is one right angle.
$A O B$ is diameter and $C$ is a point on the circle.
$∠ A C B = 90^{O}$
Using Pythagoras Theorem, we have
${A C}^{2} + {B C}^{2} = {A B}^{2}$