Question : Two circles touch each other externally at points P and AB is a direct common tangent which touches the circles at A and B, respectively. $\angle APB$ is:
Option 1: 90°
Option 2: 45°
Option 3: 100°
Option 4: 80°
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 90°
Solution : $TA = TP$ (tangent from T) $TB = TP$ (tangent from T) Now in $\triangle ATP,TA = TP$ $\therefore \angle APT = \angle PAT$ (base angles of isosceles triangle) And in $\triangle BTP,TB = TP$ $\therefore \angle BPT = \angle PBT $ (base angles of isosceles triangle) Now, in $\triangle APB$, $\angle APB + \angle PBA + \angle PAB = 180^\circ$ (angle sum property of triangle) ⇒ $\angle APB + \angle PBT + \angle PAT = 180^\circ$ ⇒ $\angle APB + \angle BPT + \angle APT = 180^\circ\ (∵ \angle APT = \angle PAT$ and $\angle BPT = \angle PBT)$ ⇒ $\angle APB + \angle APB = 180^\circ\ (∵\angle APB = \angle BPT + \angle APT)$ ⇒ $2\angle APB = 180^\circ$ $\therefore\angle APB = 90^\circ$ Hence, the correct answer is 90°.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact, and $\angle$PAB = 22°. The measure of $\angle$ABP is:
Question : Two circles with centres A and B touch each other externally, PQ is a direct common tangent which touches the circle at P and Q. If the radii of the circles are 9 cm and 4 cm, respectively, then the length of PQ (in cm) is equal to:
Question : Two circles of radii 9 cm and 4 cm, respectively, touch each other externally at point $A. PQ$ is the direct common tangent of those two circles of centres $O_1$ and $O_2$, respectively. The length of $PQ$ is equal to:
Question : Two circles C1 and C2 touch each other internally at P. Two lines PCA and PDB meet the circles C1 in C, D, and C2 in A, B respectively. If $\angle$BDC=120°, then the value of $\angle$ABP is
Question : Two circles touch each other externally at any point C. PQ is the direct common tangent to both the circles touching the circles at point P and point Q. If the radii of the circles are 36 cm and 16 cm, respectively, then the length of PQ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile