If PQ be a diamter of a circle with centre at O and if PR= RQ, then the value of `angle RPQ` is

Options

A. `30^(@)`
B. `90^(@)`
C. `60^(@)`
D. `45^(@)`

Answer

D

Explanation

PQ is a diamter of the circle with centre at O R is any point on its circumference.
`angle PRQ=90^(@)`[ by theroem-37]
Again `PR=RQ:. angle RPQ= angle RQP,.....(1) [ :.` oppoiste angles of equal sides of a triangle are equal]
Now, in `Delta PQR, angle PQR+ angle QRP+ =180^(@) [ :.` sum of three angles of a triangle is `180^(@)]`
` or,angle PQR+ angle RPQ+90^(@)=180^(@)` [ by(1) and `angle PRQ=90^(@)]`
`or, angle RPQ+ angle RPQ=90^(@)=180^(@)` [ by (1) and `angle PRQ=90^(@)]`
`or, 2 angle RPQ=180^(@)-90^(@) or, 2 angle RPQ= 90^(@)`
`or, angle RPQ=(90^(@))/(2)=45^(@) :. angle RPQ=45^(@)`
Hence (d) is correct.