Question

The following figure shows a circle with center O and a diameter AB. (i) Name the angle APB, (ii) State the measure of angle APB, (iii) If AP$=12$ cm and OA$=10$ cm; find the lengths of AB and BP, (iv) If $4AP=3PB=12$ cm, then find the radius of the circle.

• A. (i) angle in a circle, (ii) ${45}^o,$ (iii) AB$=20$ cm & BP$=16$ cm, (iv) $5$ cm.
• B. (i) angle in a semicircle, (ii) ${90}^o$,(iii) AB$=10$ cm & BP$=16$ cm,(iv) $5$ cm.
• C. (i) angle in a semicircle,(ii) ${90}^o$, (iii) AB$=20$ cm & BP$=16$ cm,(iv) $2.5$ cm.
• D. (i) angle of a sector,(ii) ${90}^o$, (iii) AB$=20$ cm & BP$=16$ cm,(iv) $2.5$ cm.
  

Answer 1

The correct option is C (i) angle in a semicircle,

(ii) ${90}^o$,

(iii) AB$=20$ cm & BP$=16$ cm,

(iv) $2.5$ cm.

The angle, subtended by a diameter of a circle, is a right angle.

Hence,

(i) angle in a semicircle,

(ii) ${90}^o$,

(iii) AB$=20$ cm & BP$=16$ cm,

(iv) 2.5cm.