In the given figure, PT touches the circle with centre O at point R. Diameter SQ is extended to meet the tangent TR at P.
Given $∠ S P R = x^{o} a n d ∠ Q R P = y^{o}$ ;
then $∠ O R S = 2 y^{o}$

True

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False

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Solution

The correct option is B False
Given,
$∠ S P R = x, ∠ Q R = y$

$∠ O S R = ∠ P R Q = y$ ( angle in alternate segment are equal)

also $∠ R O S = 2 ∠ O P T$ ( properties of circle)

$∠ R O S = 2 x$

In $Δ$ ORS
$∠ O S R + ∠ S O R + ∠ O R S = 180 ⟹ y + 2 x + ∠ O R S = 180 ⟹ ∠ O R S = 180 - (x + 2 y)$

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Similar questions

In the given figure, PT touches the circle with centre O at point R. Diameter SQ is produced to meet the tangent TR at P.

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(i) $∠ O R S = y^{o}$

(ii) write an expression connecting x and y.

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In the given figure, PT touches a circle whose centre is O at R. Diameter SQ produced meets PT at P. If $∠ S P R = x^{\circ}$ and $∠ Q R P = y^{c i r c}$ , then which of the following statements relate x and y?

In the figure, PT touches a circle with center O at R. Diameter SQ when produced meets RT at P. ∠SPR = ^o, ∠QRP = y^o, find the value of ^o + 2y^o.

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In the given figure, PT touches the circle with centre O at point R. Diameter SQ is extended to meet the tangent TR at P.Given ∠SPR=xoand∠QRP=yo;then ∠ORS=2yo

The correct option is B FalseGiven,∠SPR=x,∠QR=y∠OSR=∠PRQ=y ( angle in alternate segment are equal)also ∠ROS=2∠OPT ( properties of circle)∠ROS=2xIn Δ ORS∠OSR+∠SOR+∠ORS=180⟹y+2x+∠ORS=180⟹∠ORS=180−(x+2y)

In the given figure, PT touches the circle with centre O at point R. Diameter SQ is extended to meet the tangent TR at P.
Given $∠ S P R = x^{o} a n d ∠ Q R P = y^{o}$ ;
then $∠ O R S = 2 y^{o}$