Question

In the given figure 'O' is the center of the circle. SP and TP are the two tangents at S and T respectively. $\angle$SPT is ${50}^{\circ }$, the value of $\angle$SQT is:

• A. 125°
• B. 65°
• C. 115°
• D. None of the above

Answer 1

The correct option is C

115°

$\angle$OSP = $\angle$OTP = ${90}^{\circ }$

Therefore OSPT is cyclic

$\angle$SPT + $\angle$SOT = ${180}^{\circ }$

50 + $\angle$SOT = ${180}^{\circ }$

$\angle$SOT = ${130}^{\circ }$

Outer $\angle$SOT = ${360}^{\circ }$ – ${130}^{\circ }$ = ${230}^{\circ }$

$\angle$SQT = $\frac{1}{2}$ outer $\angle$SOT

$\angle$SQT = $\frac{1}{2}$ $\times$ ${230}^{\circ }$

$\angle$SQT = ${115}^{\circ }$