Two chords of a circle intersect each other at right angles. Chords-segment of first chord are 6 and 5, and chords-segment of second chord are 10 and 3. Then, diameter of circle is

Correct option is C

Given:

Two chords of a circle intersect each other at right angles.

The segments of the first chord are 6 and 5.

The segments of the second chord are 10 and 3.

Concept Used:

Intersecting Chords Theorem: If two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other.

Right Angle Intersection: If the chords intersect at right angles, the square of the diameter is the sum of the squares of all four segments.

Formula Used:

​$$D^2 = a^2 + b^2 + c^2 + d^2$$​​

Where a = 6, b = 5, c = 10, d = 3 and D = diameter

Solution:  

Using the formula

​$$D^2 = 6^2 + 5^2 + 10^2 + 3^2 = 36 + 25 + 100 + 9$$​​

​$$D^2 = 170$$​​

​$$D = \sqrt{170}$$​