In the following figure,if $AB = 10$,then $AC = \ldots$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) In the given figure,$OP$ is the line segment joining the center $O$ to the external point $P$. The line $OP$ is the perpendicular bisector of the chord $AB$.
Since $OP \perp AB$ and $OP$ bisects $AB$,we have $AC = CB = \frac{AB}{2}$.
Given $AB = 10$,therefore $AC = \frac{10}{2} = 5$.

Explore More

Similar Questions

The tangents drawn from a point $P$ outside $\odot(O, 5)$ touch the circle at $A$ and $B$. If $PA = 8$,then $PB = \ldots$

The chord of $\odot(O, 34)$ touches $\odot(O, 16)$. The length of the chord is .........

$P$ is a point in the exterior of $\odot(O, r)$ and the tangents from $P$ to the circle touch the circle at $X$ and $Y$. Find $m\angle XOP$,if $m\angle XPO = 65^\circ$. (in $^\circ$)

In the figure,common tangents $AB$ and $CD$ to two circles intersect at $E$. Prove that $AB = CD$.

In the figure,from an external point $P$,a tangent $PT$ and a line segment $PAB$ are drawn to a circle with centre $O$. $ON$ is perpendicular to the chord $AB$. Prove that:
$(i) \quad PA \cdot PB = PN^2 - AN^2$
$(ii) \quad PN^2 - AN^2 = OP^2 - OT^2$
$(iii) \quad PA \cdot PB = PT^2$

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo