Question

A circle with centre P and chord AB is perpendicular to diameter MN at T and T is at a distance of 9 units from N.If length of chord AB= 30,find the diameter of the circle.​

Answer 1

The diameter of the circle will be 34.

Step-by-step explanation:

See the attached diagram.

The triangle Δ PTA is a right triangle with PA = r, PT = (r - 9) and TA = 15  

Since given that AB = 30 and MN ⊥ AB and then MN will be the perpendicular bisector of AB. So, AT = BT = 15.

Again, PN = PA = radius of circle = r

Since, TN = 9, so, PT = r - 9.

Hence, (r - 9)² + 15² = r²

⇒ - 18r + 81 + 225 = 0

⇒ r = 17.  

Therefore, the diameter of the circle will be 34. (Answer)