Question

In the given figure, two chords BP and CQ are equal. If OM = 8 cm, AB = 21 cm and CN = 6 cm, then the length of OA is equal to

• A.
  20 cm
• B.
  15 cm
• C.
  17 cm
• D.
  12 cm

Answer 1

The correct option is C

17 cm
Joining O to A, we get two right-angled triangles $\Delta OMAand\Delta ONA.$

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

$\therefore NQ=CN=6cmThus,CQ=CN+NQ=6cm+6cm=12cmNow,BP=CQ\left(Given\right)\therefore BP=12cmThus,BM=MP=\frac{BP}{2}=\frac{12}{2}=6cmAlso,AB=21cm\left(Given\right)\therefore AM=AB–BM=21–6=15cm$

In $\Delta OMA,$ by Pythagoras theorem,

$(OA{)}^2=(OM{)}^2+(AM{)}^2\Rightarrow (OA{)}^2=(8{)}^2+(15{)}^2=64+225=289(\because OM=8cm)\Rightarrow OA=17cm$

Hence, the correct answer is option (c).