Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

In the adjoining figure, two circles intersect at $A$ and $B$ . The centre of the smaller circle is $O$ and lies on the circumference of the larger circle. If $PAC$ and $PBD$ are straight lines and $∠ APB = 75^{o}$ . Then, which of the following is the measure of $∠ AOB$ , $∠ ACB$ , $∠ ADB$ ?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

150^{o}

30^{o}

30^{o}

150^{o}

30^{o}

60^{o}

150^{o}

40^{o}

30^{o}

120^{o}

30^{o}

30^{o}

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Consider the given figure,
Question Image

Given that,

O

is the center of the smaller circle.

∠ APB = 75^{\circ}

.
We know that,
The angle subtended by an arc at the center of the circle has doubled the angle subtended at any point of the circle.
So,

∠ AOB = 2 ∠ APB

⟹

∠ AOB = 2 \times 75^{\circ}

⟹

∠ AOB = 150^{\circ}

Now, since

ACOB

is a cyclic quadrilateral,

∠ ACB + ∠ AOB = 180^{\circ}

...[Opposite angles of a cyclic quadrilateral are supplementary]

\Rightarrow ∠ ACB + 150^{\circ} = 180^{\circ}

\Rightarrow ∠ ACB = 180^{\circ} - 150^{\circ}

\Rightarrow ∠ ACB = 30^{\circ}

Also, since AOBD is a cyclic quadrilateral,

∠ ADB + ∠ AOB = 180^{\circ}

...[Opposite angles of cyclic quadrilateral are supplementary]

\Rightarrow ∠ ADB + 150^{\circ} = 180^{\circ}

\Rightarrow ∠ ADB = 180^{\circ} - 150^{\circ}

\Rightarrow ∠ ADB = 30^{\circ}

.
Hence,

∠ AOB = 150^{\circ}

∠ ACB = 30^{\circ}

and

∠ ADB = 30^{\circ}

.
Therefore, option 1 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!