6 Views

Question : PT is a tangent at the point R on a circle with centre O. SQ is a diameter, which when produced meets the tangent PT at P. If $\angle$SPT = 32$^\circ$, then what will be the measure of $\angle$QRP?

Option 1: $58^\circ$

Option 2: $30^\circ$

Option 3: $29^\circ$

Option 4: $32^\circ$


Team Careers360 15th Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

Correct Answer: $29^\circ$


Solution :
Given, $\angle SPT = 32^\circ$
$OR$ is perpendicular to $PT$, so $\angle ORP = 90^\circ$
Let $\angle QRP = \theta$
As we know, the sum of two interior opposite angles of a triangle is equal to its exterior angle.
So, $\angle OQR = 32^\circ + \theta$
⇒ $\angle OQR = \angle ORQ = 32^\circ + \theta$ [same radii]
Now,
$\angle ORP = \angle ORQ + \angle QRP$
⇒ $90^\circ = 32^\circ + \theta + \theta$
⇒ $2\theta = 90^\circ – 32^\circ = 58^\circ$
⇒ $\theta = \frac{58^\circ}{2} = 29^\circ$
So, $\angle QRP = 29^\circ$
Hence, the correct answer is $29^\circ$.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books