Question

In the given figure, AB and CD are diameters of the circle and AC=4 cm and $\angle DPB={45}^{\circ }$

Find the radius if the circle.

• A. $4\sqrt{2}$ cm
• B. $7\sqrt{2}$ cm
• C. $2\sqrt{2}$ cm
• D. $3\sqrt{2}$ cm

Answer 1

The correct option is C

$2\sqrt{2}$ cm

$\angle DPB={45}^{\circ }$ (Given)

$\angle DOB=2\angle DPB={90}^{\circ }$

(As angle subtended by an arc at the centre is twice the angle subtended by it at the circumference)

So,$\angle DOB=\angle AOC={90}^{\circ }$ (vertically opposite angles)

Now,In $\Delta AOC$

OA=OC and, $\angle AOC={90}^{\circ }$

AC=4 cm (Given)

So, Let OA=OC=r

So,$O{A}^2+O{C}^2=A{C}^2$

$r^2+r^2=A{C}^2$

$2r^2=16$

$r^2=8$

r=$2\sqrt{2}$cm