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-

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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Intersection between Tangent and Secant

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?

Open in App

Solution

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)

Suggest Corrections

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.

Given $∠ S P R = x^{o}$ and $∠ Q R P = y^{o}$

prove that:

(i) $∠ O R S = y^{o}$

(ii) write an expression connecting x and y.

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?

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

Join BYJU'S Learning Program

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?

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?