Question

25 points! Find the value of X.

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}$

In the Triangle BCD, Angle B is 90° since tangent and radius are perpendicular to one another.

Now, let's find Angle C using Angle sum property of a triangle.

$\qquad \tt \dashrightarrow \:\angle C + \angle B + \angle D = 180$

$\qquad \tt \dashrightarrow \:\angle C + 90 + 45= 180$

$\qquad \tt \dashrightarrow \:\angle C + 135= 180$

$\qquad \tt \dashrightarrow \:\angle C= 180 - 135$

$\qquad \tt \dashrightarrow \:\angle C= 45 \degree$

Now, we know that Angle made by an arc on the centre is twice the Angle made by same arc on boundary of circle, hence we can infer that :

$\qquad \tt \dashrightarrow \:2\angle C = 10x$

$\qquad \tt \dashrightarrow \:10x = 2 \times 45$

$\qquad \tt \dashrightarrow \:x = 90 \div 10$

$\qquad \tt \dashrightarrow \:x = 9$

So, the required value of x is 9