Angles subtended by chords $A C$ and $B C$ at the centre $O$ of the circle are $55^{o}$ and $155^{o}$ respectively. What is the measure of $∠ A C B$ ?

65^{o}

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

75^{o}

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

105^{o}

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

135^{o}

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

Open in App

Solution

The correct option is B $75^{o}$
$O A = O B = O C = r a d i u s$
In $△ O B C$
Since $O B = O C$
$∠ O B C = ∠ O C B$
$∠ B O C = 155$
$∠ O B C + ∠ O C B + ∠ B O C = 180$
$2 ∠ O C B = 180 - 155$
$∠ O C B = 12.5$
Similarly in $△ O A C$
$2 ∠ O C A = 180 - 55$
$∠ O C A = 62.5$
$2 ∠ O C B = 180 - 155$
$∠ O C B = 12.5$
SCB = $2 ∠ O C B = 180 - 155$
$∠ O C B = 12.5$
OCB + $2 ∠ O C B = 180 - 155$
$∠ O C B = {12.5}^{\circ}$

$O C A = 12.5 + 62.5 = 75^{\circ}$

Suggest Corrections

Similar questions

$A, B$ and $C$ are three points on a circle such that the angles subtended by the chords $A B$ and $A C$ at the centre $O$ are $90^{\circ}$ and $110^{\circ}$ respectively. Then the measure of angle $B A C$ is

Q. Two chords

A B

and

A C

of a circle subtends angles equal to

90^{o}

and

150^{o}

, respectively at the centre. Find

∠ B A C

, if

A B

and

A C

lie on the opposite sides of the centre.

Q. Two chords

A B

and

A C

of a circle subtends angles equal to

90^{\circ}

and

150^{\circ}

respectively at the centre. Find

∠ B A C

In figure $A, B, C$ are three points on a circle such that the angles subtended by the chord $A B$ and $A C$ at the centre $O$ are $80^{\circ}$ and $120^{\circ}$ respectively. Determine $∠ B A C$ and the degree measure of arc $B P C$ .

Q. Fill In The Blanks

Two chords AB and AC of a circle are on the opposite sides of the centre. If AB and AC subtend angles equal to 90^∘ and 150^∘ respectively at the centre, then ∠BAC = _________.

Join BYJU'S Learning Program

Angles subtended by chords AC and BC at the centre O of the circle are 55o and 155o respectively. What is the measure of ∠ACB?

Angles subtended by chords $A C$ and $B C$ at the centre $O$ of the circle are $55^{o}$ and $155^{o}$ respectively. What is the measure of $∠ A C B$ ?