General Aptitude TestQuantitative ReasoningGeometry

In a triangle ABC if ∠ B=90^°, BC = 8 cm and AB = 15 cm, then radius…

In a $\triangle ABC$ if $\angle B=90^{\circ}$, BC = 8 cm and AB = 15 cm, then radius r of the incircle of $\triangle ABC$ is:

Answer & explanation

Correct answer: option 3

Triangle ABC is right angled at B.

AB = 15 cm

BC = 8 cm

Applying Pythagoras theorem,

AC^2=AB^2+BC^2=(15)^2+(8)^2=(225+64)=289

AC = 17

Since the circle is inscribed, quadrilateral made with the centre of the circle, O, Point B, P and Q make a square

$B P = B Q = x c m$ .

Since the tangents to a circle from an exterior point are equal in length,

we have AR = AP and CR = CQ.

Now, AR = AP = (AB - BP) = (15 – x) cm

CR = CQ = (BC – BQ) = (8 - x) cm.

$A C = A R + C R \Rightarrow 17 = (15 - x) + (8 - x) \Rightarrow 2 x = 6 \Rightarrow x = 3$ .

Hence, the radius of the inscribed circle is 3 cm.

The correct answer is Option (3) → 3 cm