**GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Long Question**

**Exam Question:**

In a right triangle ABC, right-angled at B, BC = 12cm and AB = 5cm. What is the radius of the circle inscribed in the triangle (in cm)?

**Answer:**

For GCSE Mathematics, you should know:

First, let's check out our given information.**AB = 5cm** and **BC = 12cm**.

By using Pythagoras' theorem,

**AC**^{2}** = AB**^{2}** + AC**^{2}

= 52 + 122

= 25 + 144

= 169

Therefore, AC = 13 units.

Next, we have to remember a crucial point regarding tangents:

*"Two tangents drawn to a circle from the same point exterior of the circle are of ***equal lengths***."*

Looking at the graph, we can see:

**AM = AQ = a**

Similarly, **MB = BP = b** and** PC = CQ = c**.

We now know that:

AB = a + b = 5

BC = b + c = 12

AC = a + c = 13

By using the method of solving simulatenous equations, we get:**a = 3, b = 2 and c = 10.**

Another rule to remember is that** tangents are always perpendicular to the radius**.

Thus, OMBP is found to be a square, with sides b.

From this, we can see that the radius' length in the right-angled triangle is __ 2cm__.

The following sketch is for your reference.

Work hard for your GCSE Mathematics examination!

End of analysis. Great!