Question

If AB AC PQ are tangents to the circle with centre X and radius XB where AB = 5cm. What will be the perimeter of triangle APQ?

Answer 1

Perimeter of triangle APQ is `10cm.`

Explanation:

Consider the following diagram, where two tangents `AB` and `AC` are drawn from an external point `A` to a circle with center `X`. We have `AB=AC=5cm.`. Now draw another tangent `PQ` to touch circle at `R`. We have to find perimetero triangle `APQ`.

As tangents are drawn from an external point `A`, we have `AB=AC`. Similarly, `P` and `Q` are external points and hence tangents from it too would be equal.

Therefore, `PC=PR` and `QB=QR` and perimeter of triangle `APQ` is

`AP+PQ+QA`

= `AP+PR+RQ+QA`

= `AP+PC+QB+QA`

= `AC+AB`

= `5+5=10cm`