Question : If in $\triangle$ XYZ, XY = 4 cm and XZ = 5 cm and Q is a point on YZ such that XQ bisects $\angle X$, then YQ : QZ is:
Option 1: 2 : 3
Option 2: 3 : 2
Option 3: 5 : 4
Option 4: 4 : 5
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Correct Answer: 4 : 5
Solution : In $\triangle$ XYZ, XY= 4 cm and XZ = 5 cm Since XQ bisects $\angle X$, ⇒ XY : XZ = YQ : QZ $\therefore$ YQ : QZ = 4 : 5 Hence, the correct answer is 4 : 5.
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Question : $\triangle$ XYZ is a right-angled triangle and $\angle$Y = 90° If XY = 2.5 cm and YZ = 6 cm, then the circumradius of $\triangle$XYZ is:
Question : In a triangle $XYZ$ right-angled at $Y$, if $XY=2\sqrt{6}$ and $XZ-YZ=2$, then $\sec X+\tan X$ is:
Question : In $\triangle X Y Z, \angle X=90^{\circ}, YZ=15 \mathrm{~cm}$, and $X Z=12 \mathrm{~cm}$. Then find $\cos Y$.
Question : In triangle XYZ, G is the centroid. If XY = 11 cm, YZ = 14 cm, and XZ = 7 cm, then what is the value of GM?
Question : In $\triangle P Q R$, $\angle Q=90^{\circ}$, $PQ=8$ cm and $\angle P R Q=45^{\circ}$ Find the length of $QR$.
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