#### Question

In the figure given below, O is the center of the circle of the circle and SP is a tangent. if ∠SRT=65°, find the value of x, y and Z.

#### Solution

`TS ⊥ SP,`

`⇒ ∠TSR=90°`

`"In" ΔTSR, `

`∠TSR+∠TRS+∠RTS=180°`

`⇒90°+65°+x=180°`

`⇒x=180°-90°-65°`

`⇒x=25°`

`"Now", y=2x .............("Angle subtended at the center is double that of the angle subtended by the arc at the same centre")`

`⇒y=2xx25°`

`⇒y=50°`

`"In" Δ OSP,`

`∠OSP+∠SPO+∠POS-=180°`

`⇒90°+z+50°=180°`

`⇒z=180°-140°`

`⇒z=40°`

`"Hence", x=25°,y=50° and Z=40°`

Is there an error in this question or solution?

Solution In the Figure Given Below, O is the Center of the Circle of the Circle and Sp is a Tangent. If ∠Srt=65°, Find the Value of X, Y and Z. Concept: Number of Tangents from a Point on a Circle.