Question : Two circles touch externally at P. QR is a common tangent of the circle touching the circles at Q and R. Then, the measure of $\angle QPR$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $90^{\circ}$

Option 4: $45^{\circ}$

Question : Two circles with radii of 25 cm and 9 cm touch each other externally. The length of the direct common tangent is:

Option 1: 34 cm

Option 2: 30 cm

Option 3: 36 cm

Option 4: 32 cm

Question : Two circles of radii 8 cm and 3 cm, respectively, are 13 cm apart. AB is a direct common tangent touch to both the circles at A and B respectively then the length of AB is:

Option 1: 10 cm

Option 2: 12 cm

Option 3: 8 cm

Option 4: 6 cm

Question : PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that $\angle {APB}=100^{\circ}$, then $\angle {OAB}$ is equal to:

Option 1: $45^{\circ}$

Option 2: $35^{\circ}$

Option 3: $70^{\circ}$

Option 4: $50^{\circ}$

Question : Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is:

Option 1: 8.5 cm

Option 2: $\frac{8}{\sqrt{2}}$ cm

Option 3: $8\sqrt{2}$ cm

Option 4: 8 cm