Question

What is the value of $l+m$ in the given figure?

• A. Greater than ${90}^o$
• B. Less than ${90}^o$
• C. Equal to ${180}^o$
• D. Equal to ${90}^o$

Answer 1

Answer: (D)

$\angle POQ=2\angle PRQ$

Because Angle made by an arc at the center is twice the angle made by an arc a any point on the circle

$⟹\angle POQ=2l$

In $△POQ$

$OP=OQ=radius$

$⟹\angle OPQ=\angle OQP=m$

$\angle POQ+\angle OPQ+\angle OQP=180$

$⟹2l+m+m=180$

$l+m={90}^{\circ }$$\angle POQ=2\angle PRQ$

Because Angle made by an arc at the center is twice the angle made by an arc a any point on the circle

$⟹\angle POQ=2l$

In $△POQ$

$OP=OQ=radius$

$⟹\angle OPQ=\angle OQP=m$

$\angle POQ+\angle OPQ+\angle OQP=180$

$⟹2l+m+m=180$

$l+m={90}^{\circ }$