Question

Q1.Two concentric circles of radii 15 cm, 12 cm are drawn. Find the length of chord of larger circle which touches the smaller circle.

Answer 1

Explanation:

✬ Chord = 18 cm ✬

Step-by-step explanation:

Given:

• Radii of two concentric circles is 15 and 12 cm respectively.

To Find:

• Length of chord of larger circle which touches the smaller circle ?

Solution: Let A be the bigger circle of radius 15 cm and A' be the smaller circle of radius 12 cm. O is common centre of both the circles.

Let BC be a chord of circle A , passing by touching the smaller circle. Join O to C & B.

Here we have

OC = OB = 15 cm (radii of A)

OD = 12 cm (radius of A')

BC = (chord of A)

OD is also perpendicular to BC.

∠ODC = ∠ODB = 90°

BD = DC (OD bisects BD)

[ See figure for understanding ]

Now in right angled ∆ODC we have

OC {hypotenuse}

DC {base}

OD {perpendicular}

Using Pythagoras theorem

★ H² = Perpendicular² + Base² ★

⟹ OC² = OD² + DC²

⟹ 15² = 12² + DC²

⟹ 225 – 144 = DC²

⟹ √81 = DC

⟹ 9 = DC

∴ BD = DC = 9 cm

Hence, BC = 9 + 9 = 18 cm. This is required length of chord which touches the smaller circle.