Question
Two concentric circles with center O have A, B, C, D as the points of intersection with the lines L shown in the figure. If AD = 12 cm and BC s = 8 cm, find the lengths of AB, CD, AC and BD.
✓
Answer
Since, OM ⊥ BC
BM = CM = $\frac{1}{2} BC =4 cm$
also, OM ⊥ AD
So, AM = DM = $\frac{1}{2} AD =6 cm$
now, AB = AM - BM = ( 6 - 4 ) cm = 2 cm
CD = DM - CM = ( 6 - 4 ) cm = 2 cm
∴ AC = AB + BC = ( 2 + 8 ) cm = 10 cm
and BD = BC + CD = ( 8 + 2 ) cm = 10 cm
BM = CM = $\frac{1}{2} BC =4 cm$
also, OM ⊥ AD
So, AM = DM = $\frac{1}{2} AD =6 cm$
now, AB = AM - BM = ( 6 - 4 ) cm = 2 cm
CD = DM - CM = ( 6 - 4 ) cm = 2 cm
∴ AC = AB + BC = ( 2 + 8 ) cm = 10 cm
and BD = BC + CD = ( 8 + 2 ) cm = 10 cm
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The following table givens the age of 50 student of a class . find the arithmetic mean of thier agges.
| Age- Years | 16-18 | 18-20 | 20-22 | 22-24 | 24-26 |
| No.of students | 2 | 7 | 21 | 17 | 3 |
TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Prove that AP bisects the angle TAB.
Mrs. Goswami deposits Rs. 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value. (2009)
If $x – 2$ is a factor of $2x^3 - x^2 - px - 2.$
with the value of p, factorize the above expression completely.
→with the value of p, factorize the above expression completely.
A triangle $\text{ABC}$ is right angles at $B;$ find the value of
$\frac{\sec A \operatorname{cosec} A-\tan A \cot C}{\sin B}$
→$\frac{\sec A \operatorname{cosec} A-\tan A \cot C}{\sin B}$
In each of the following determine whether the given values are solutions of the equation or not.
$x^2 + 6x + 5 = 0; x = -1, x = -5$
→$x^2 + 6x + 5 = 0; x = -1, x = -5$
Solve the following equation by using formula :
$x^2 + (4 – 3a)x – 12a = 0$
→$x^2 + (4 – 3a)x – 12a = 0$
A company pays $7 \%$ dividend. For how much should a man buy a ₹ $ 100$ shares for getting $8 \%$ on his investment?
→Find the two numbers such that their mean proprtional is $24$ and the third proportinal is $1,536.$
→If $0^\circ < A < 90^\circ ;$ Find $A,$ if :$\frac{\cos A}{1-\sin A}+\frac{\cos A}{1+\sin A}=4$
→