Share
Notifications

View all notifications
Advertisement

If Pq is a Tangent to the Circle at R; Calculate: - Mathematics

Login
Create free account


      Forgot password?

Question

If PQ is a tangent to the circle at R; calculate:
(i) ∠PRS

(ii) ∠ROT 

Given :  O is the centre of the circle and angle TRQ = 30°

Solution

PQ is a tangent and OR is the radius.

∴ OR ⊥  PQ

∴ ∠ ORT = 90°

⇒∠ TRQ = 90° - 30° = 60°

But in Δ OTR ,

OT = OR (Radii of the same circle)

∴ ∠ OTR = 60° Or ∠ STR = 60°

But,

∠ PRS = ∠ STR = 60 (Angle in the alternate segment)

In ΔORT,

∠ ORT  = 60°

∠ OTR =60°

∴ ∠ ROT = 180° - (60° +60° ) 

∴ ∠ ROT = 180°  - 120° = 60°

  Is there an error in this question or solution?
Advertisement

APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (B) | Q: 4 | Page no. 283
Advertisement
If Pq is a Tangent to the Circle at R; Calculate: Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.
Advertisement
View in app×