Question
In Figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
✓
Answer
Given common tangent AB and CD to two circles intersecting at E. To prove AB = CD
Proof: EA = EC ...(i) [the lengths of tangents drawn from an internal point to a circle are equal] EB = ED ...(ii) On adding Eqs. (i) and (ii), we get EA + EB = EC + ED ⇒ AB = CD Hence proved.
Proof: EA = EC ...(i) [the lengths of tangents drawn from an internal point to a circle are equal] EB = ED ...(ii) On adding Eqs. (i) and (ii), we get EA + EB = EC + ED ⇒ AB = CD Hence proved.
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 product of three consecutive positive integers is divisible by 6". Is this statement true or false"? Justify your answer.
A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at 60 to the horizontal. Find the length of the string to the nearest metre.
Determine the set of values of k for which the given following quadratic has real root:
$2x^2 + kx + 2 = 0$
→$2x^2 + kx + 2 = 0$
Prove the following identities:
$1+\frac{\cot^2\theta}{(1+\text{cosec }\theta)}=\text{sec}\theta$
→$1+\frac{\cot^2\theta}{(1+\text{cosec }\theta)}=\text{sec}\theta$
Find the value of k for which the following systems of linear equations has an infinite number of solutions:
$2x + 3y = 7,$
$(k - 1)x + (k + 2)y = 3k.$
→$2x + 3y = 7,$
$(k - 1)x + (k + 2)y = 3k.$
D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that DE || BC:
If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC.
→If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC.
If the area of two similar triangles are equal, prove that they are congruent.
If $\text{ABC}$ is isosceles with $AB = AC,$ prove that the tangent at $A$ to the circumcircle of $\text{ABC}$ is parallel to $BC$.
→Half of the difference between two numbers is $2$ . The sum of the greater number and twice the smaller number is $13$. Find the numbers.
→Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.
→