AI Mentor

Check Your IQ

Free Expert Demo

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 figure, O is the centre of the circle. Determine and $∠$ AOB if PA and PB are tangents and $∠$ ABP $= 75 °$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

∠

ABP

= 52.5 °

and

∠

ABP

= 127.5 °

∠

ABP

= 50.5 °

and

∠

ABP

= 127.5 °

∠

ABP

= 52.5 °

and

∠

ABP

= 128.5 °

∠

ABP

= 52.5 °

and

∠

ABP

= 120.5 °

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that,

∠

APB = 75°.
Question Image

PA and PB are the tangents to the circle from P at A and B respectively and OA and OB are the radii of the circle.
Hence, OA _|_ PA and OB_|_ PB.
Now,

∠

OAP =

∠

OBP = 90°.
In quadrilateral AOBP,
Sum of all the angles of a quadrilateral is 360°.

∠

ABP +

∠

OAP +

∠

OBP +

∠

AOB = 360°

\Rightarrow

75° + 90° + 90° +

∠

AOB = 360°

\Rightarrow

255° +

∠

AOB = 360°

∠

AOB = 360° - 255°

∠

AOB = 105°
We know that angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle. Consider the minor arc AB, then