Question

Chord AC intersects chord BD at point P in circle Z.

AP=12 m
DP=5 m
PC=6 m

What is BP?
Enter your answer as a decimal in the box.

_______ m

Answer 1

`BP=14.4` meters.

Explanation:

We have been given a circle and we are asked to find the measure of segment BP.

We can see that AC and BD are chords of our given circle.

The intersecting chords theorem states that when two chords intersect inside a circle, then product of their segments are always equal.

Using Intersecting chords theorem, we will get an equation as:

`BP*PD=AP*PC`

Substituting our given values in above equation we will get,

`BP*5=12*6`

`BP*5=72`

Dividing both sides of our equation by 5 we will get,

`(BP*5)/(5)=(72)/(5)`

`BP=14.4`

Therefore, the length of segment BP is 14.4 meters.

Answer 2

In this question, we have to use the intersecting chord theorem, and the formula which is

`AP * CP = BP * DP`

In the given circle, values of AP, CP and DP are 12m, 6m and 5m respectively .

Substituting the values in the formula, we will get

`12*6 = 5BP`

Dividing both sides by 5

`BP = (72)/(5) = 14.4 m`