You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Angle Subtended by an Arc of a Circle on the Circle and at the Center

Let O be th...

Question

Let $O$ be the centre of a circle, with $P Q$ as a diameter, then prove that $∠ P R Q = 90^{o}$ (OR) Prove that angle subtended by semi-circle is $90^{o}$ .

Open in App

Solution

$∠ P O Q i s 180^{\circ}$ since it is a straight line and angle subtended by arc of a circle at its center is twice the angle formed by the same arc of a point on the circle.

$∠ P O Q = 2 ∠ P R Q$

$∠ P R Q = \frac{180^{o}}{2} = 90^{o}$

Where R is any point on the circle.

Suggest Corrections

Similar questions

Q. Prove that the angle subtend in a semi circle is always

90^{o}

A, B, C

are point in the circle with centre

O

. If

O C A = x

then find

∠ O A C

. Prove that

∠ O C A

∠ A B C = 90^{o}

Q. Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle

Q. Let

Γ

be a circle with centre

O .

Let

Λ

be another circle passing through

O

and intersecting

Γ

at points

A

and

B .

A diameter CD of at points A and B. A diameter

C D

Γ

intersects

Λ

at a point

P

different from

O .

Prove intersects

Λ

at a point P different from O. Prove that

∠

APC =

∠

BPD .

Prove that the parallelogram circumscribing a circle is a rhombus.
OR
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Join BYJU'S Learning Program

Let O be the centre of a circle, with PQ as a diameter, then prove that ∠PRQ=90o (OR) Prove that angle subtended by semi-circle is 90o.

∠POQis180∘ since it is a straight line and angle subtended by arc of a circle at its center is twice the angle formed by the same arc of a point on the circle. ∠POQ=2∠PRQ ∠PRQ=180o2=90o Where R is any point on the circle.

Let $O$ be the centre of a circle, with $P Q$ as a diameter, then prove that $∠ P R Q = 90^{o}$ (OR) Prove that angle subtended by semi-circle is $90^{o}$ .

$∠ P O Q i s 180^{\circ}$ since it is a straight line and angle subtended by arc of a circle at its center is twice the angle formed by the same arc of a point on the circle.

$∠ P O Q = 2 ∠ P R Q$

$∠ P R Q = \frac{180^{o}}{2} = 90^{o}$

Where R is any point on the circle.