Question

In circle M shown, chords GH and EF intersect at K such that EK  5 and FK  6 . If GK  3 , then which of the following is the length of GH ?

Options:
(1) 8
(2) 10
(3) 13
(4) 15

Answer 1

The length of the GH segment is 13

Explanation:

For solving this problem we need to remember some of the circle corollaries-

When two-chord intersects each other, the product of the chord segments are equal

The above corollary can be easily understood by looking at a diagram attached below-

In the figure, EF and GH are two chords intersecting at K

Thus, EK*KF= GK*KH

Values of the EK, KF, GK are given as 5, 6 and 3 respectively

Substituting the values we get

5*6=3*KH

KH= 10

We know that GH= GK+KH

Thus GH= 3+10= 13