Where do I make Chord?

Geometry Level 3

Let $XY$ is a chord of length $12 \text{ cm}$ in a circle of radius $10\text{ cm}$ and the tangents at $X$ and $Y$ intersect at point $C$ .

Find the length of $CX$ (in $\text{cm}$ ).

The answer is 7.5.

2 solutions

Akshat Sharda
Jan 31, 2016

Let $O$ be the centre of circle and $XY$ intersect $OC$ at $Z$ . So, $OZ=8 \text{ cm}$ .

In $\triangle OXC$ , $\boxed{10^2+CX^2=CO^2=(CZ+8)^2}\rightarrow 1$ .

In $\triangle CZX$ , $\boxed{CZ^2+6^2=CX^2}\rightarrow 2$ .

By solving $1$ and $2$ , $CX=\boxed{7.5}$ .

Very Nice! This is same question from class 10th NCERT.

A Former Brilliant Member - 5 years, 4 months ago

I tried using congruence and aa similarity. Can you please tell me how you got the second equation.

abhigyan adarsh - 5 years, 3 months ago

Abhigyan Adarsh
Feb 19, 2016

Let O be the center and XY intersect OC at Z. Now 🔺 OXC ~ 🔺 OZX by AA similarity since angle XOZ = angle COX. and angle OZX = angle OXC. Hence OZ/ZX=OX/CX. => 8/6=10/ CX =>CX=7.5. Answer

Where do I make Chord?

The answer is 7.5.

2 solutions

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