KnowledgeBoat Logo

Mathematics

In the figure (i) given below, two circles with centers C, D intersect in points P, Q. If length of common chord is 6 cm and CP = 5 cm, DP = 4 cm, calculate the distance CD correct to two decimal places.

In figure, two circles with centers C, D intersect in points P, Q. If length of common chord is 6 cm and CP = 5 cm, DP = 4 cm, calculate the distance CD correct to two decimal places. Circle, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Circles

10 Likes

Answer

From figure,

In figure, two circles with centers C, D intersect in points P, Q. If length of common chord is 6 cm and CP = 5 cm, DP = 4 cm, calculate the distance CD correct to two decimal places. Circle, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

PM = MQ = 62\dfrac{6}{2} = 3 cm.

In right △CMP,

⇒ CP2 = CM2 + PM2 (By pythagoras theorem)

⇒ 52 = CM2 + 32

⇒ CM2 = 25 - 9

⇒ CM2 = 16

⇒ CM = 16\sqrt{16} = 4 cm.

In right △DMP,

⇒ DP2 = DM2 + PM2 (By pythagoras theorem)

⇒ 42 = DM2 + 32

⇒ DM2 = 16 - 9

⇒ DM2 = 7

⇒ DM = 7\sqrt{7} = 2.65 cm.

CD = CM + MD = 4 + 2.65 = 6.65 cm.

Hence, CD = 6.65 cm.

Answered By

4 Likes


Related Questions