#### 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?

Solution 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° 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.