In the given figure- PT touches a circle whose centre is O at R- Diameter SQ produced meets PT at P- If - SPR - x - and - QRP - y circ- then which of the following statements relate x and y -A- x-2 y-90-B- x-y-90-C- x-2 y-45-D- x-2 y

The correct option is A x+2y=90^∘ PT is a tangent to the circle (given) ∠ QRP = ∠ QSR =y^∘ (angle in the alternate segment are equal) QS is diameter of the ...

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Byju's Answer

Standard X

Mathematics

Tangents from External Points

In the given ...

Question

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?

$x + 2 y = 90^{\circ}$

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$x + y = 90^{\circ}$

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$x + 2 y = 45^{\circ}$

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x=2y

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Solution

The correct option is A
$x + 2 y = 90^{\circ}$

PT is a tangent to the circle (given)

$∠ Q R P = ∠ Q S R = y^{\circ}$ (angle in the alternate segment are equal)

QS is diameter of the circle (given)

$∠ Q R S = 90^{\circ}$ (angle in the semi circle)

In $△ P S R, x + y + 90^{\circ} + y = 180^{\circ}$ (sum of angles of a triangle)

$∴ x + 2 y = 90^{\circ}$ Hence (A)

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Similar questions

In the given, PT touches the circle with centre Q at point R. Diameter SQ is product to meet the tangent TR at P. $∠ S P R = x^{\circ}$ and $∠ Q R P = y^{\circ}$
Which one of the following statements are true?

Q. In the figure,

P T

touches the circle at

R

whose centre is

0

. Diameter

S Q

when produced meets

P T

P

. Given

∠ S P R = x^{o}

and

∠ O R P = y^{o}

. Then,

Q. 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}

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.

$In the given figure, PT is a tangent of a circle, with centre O, at point R. If diameter SQ is produced, it meets with PT at point P with ∠ S P R = x and ∠ Q S R = y, then find the value of x + 2 y .$

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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 ∠SPR=x∘ and ∠QRP=ycirc, then which of the following statements relate x and y?

The correct option is A x+2y=90∘ PT is a tangent to the circle (given) ∠QRP=∠QSR=y∘ (angle in the alternate segment are equal) QS is diameter of the circle (given) ∠QRS=90∘ (angle in the semi circle) In △PSR,x+y+90∘+y=180∘ (sum of angles of a triangle) ∴x+2y=90∘ Hence (A)

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?