Question

Two circles touch each other externally at point P. OA and OB are tangents to the two circles (as shown) and OA = 10.

Statement (1): OB = 10 cm.

Statement (2): On joining O and P, tangent OP = tangent OA and tangent OP = tangent OB.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

Join OP.

We know that,

If two tangents are drawn to a circle from an exterior point, the tangents are equal in length.

From figure,

O is the point from which, OA and OP are two tangents to the circle with centre Q'.

So, OA = OP .......(1)

Similarly, from point O, OB and OP are two tangents to the circle with centre Q.

So, OB = OP ......(2)

From (1) and (2), we have

⇒ OA = OB

⇒ OB = 10 cm

∴ Both the statements are true.