wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If angle between two tangents drawn from a point P to a circle of radius a and center O is 90°, then OP=a2. Write ‘True’ or ‘False’ and justify your answer.


A
True
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
False
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A True

Verify the given statement

Let PT and PR be the tangents drawn from point P to the circle.

According to given condition TPR=90

The line joining the centre and the point P is an angle bisector of the TPR

So, TPO=OPR=45

We know that the tangent to a circle is perpendicular to the radius at the point of contact.

So, OTTP

In right angled TPO

sin45=OTOP

12=aOP

OP=a2

Hence the given statement is true.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
The Length of Two Tangents Drawn From an Exterior Point to a Circle are Equal
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon